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Our aim is to help students learn subjects like physics, maths and science for students in schoolcollege and those preparing for competitive exams. All right reserved. All material given in this chxpter is a property of physicscatalyst. Playing With Numbers What are Factors? A factor of a number is an exact divisor of that number Example 1. Every multiple of a number is greater than or equal to that number. Prime Numbers The numbers other than 1 whose only factors are 1 and the number byjuz are called Prime numbers.

Example: 2, 3, 5, 7, 11 ,13 We can find list of prime numbers till using Sieve of Eratosthenes method Step 1 : Cross out 1 because it is not a prime number.

Step 2 : Encircle 2, cross out all the multiples of 2, other than 2 itself, i. Step 3: You will find that the next uncrossed number is 3. Encircle 3 and cross out all the multiples of 3, other than 3. Step 4: The next uncrossed number is 5.

Encircle 5 and cross out all the multiples of 5 other than 5. Step 5: Continue this process till all the numbers in the list are either encircled or crossed. All the encircled numbers are prime byhus. All the crossed-out numbers, other than 1 are composite numbers Composite Numbers Numbers having more than two factors 1 and itself Byjus Class 10 Maths Chapter 3 Review are called Composite numbers Example: 4, 6, 8 ,9�. Important points about prime numbers based on definition of odd and even numbers 1.

We can find common factors and multiple between 2 or more numbers Example 1 Common factors of 4,12, and 16 Factors of 4 are 1, 2 and 4. Factors of 12 are 1, 2, 3, 4, 6 and Factors of 16 are 1, 2, 4, 8 and Clearly, 1, 2 and 4 are the common factors of 4, 12, and Important Note Two numbers having only 1 as a common factor are called co-prime byjus class 6 maths chapter 3 visions Example 3 and 4 are co-prime Divisibility Rules based on factors and Multiple, co -prime 1 if a number is divisible by another number then it byjus class 6 maths chapter 3 visions divisible by each of the factors of that number Example 36, is divisible by 18 Now if we find factors of 18 i.

Now it is divisible by 15 also 3 If two given numbers are divisible by a byjus class 6 maths chapter 3 visions, then their sum is also divisible by that number.

Find the prime factorisation of the numbers b. Choose the common factors in them c. Physicscatalyst Our aim is to help students learn subjects byjus class 6 maths chapter 3 visions physics, maths and science for students in schoolmarhs and those preparing for competitive exams.

Legal Privacy Policy Terms of Use. Email us at [email protected]. A number is divisible by 3 if the byjus class 6 maths chapter 3 visions of the digits is a multiple of btjus, then the number is divisible by 3.

A number is divisible by 6 if a number is divisible by 2 and 3. A number is divisible by 9, if the sum of the digits of a number is divisible by 9. A number is divisible by 11 if the difference between the sum of the digits at odd places from the right and the sum of the digits at even places from the right of the number is either 0 or divisible by byjks.

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What is the sum of any two: a Odd numbers? Solution: a The sum of any two odd numbers is even. State whether the following statements are True or False. The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to Solution: The required pair of prime numbers having same digits are: 17 and 71 , 37 and 73 , 79 and Write down separately the prime and composite numbers less than Solution: Prime numbers less than 20 are: 2, 3, 5, 7, 11, 13, 17 and 19 Composite numbers less than 20 are: 4, 6, 8, 9, 10, 12, 14, 15, 16 and What is the greatest prime number between 1 and 10?

Solution: The greatest prime number between 1 and 10 is 7. Express the following as the sum of two odd primes. Give three pairs of prime numbers whose difference is 2. Which of the following numbers are prime? Write seven consecutive composite numbers less than so that there is no prime number between them. Solution: Required seven consecutive composite numbers are: 90, 91, 92, 93, 94, 95 and Express each of the following numbers as the sum of three odd primes.

Write five pairs of prime numbers less than 20 whose sum is divisible by 5. Fill in the blanks. Solution: a prime number b composite number c prime, composite d 2 e 4 f 2. Using divisibility tests, determine which of the following numbers are divisible by 2, by 3, by 4, by 5, by 6, by 8, by 9, by 10, by 11 Say, Yes or No Solution:.

Using divisibility tests, determine which of following numbers are divisible by 4; by 8. Remainder 0. Hence, is divisible by 4. Remainder 4. Hence, is not divisible by 8. Hence, is divisible by. Hence, is divisible by 8. Hence, is not divisible by 4. Using divisibility tests, determine which of the following numbers are divisible by 6: a b c d e f g h i j Solution: We know that a number is divisible by 6 if it is also divisible by both 2 and 3.

So, it is divisible by 2. Hence, the given number is divisible by 6. Hence, the given number is not divisible by 6. So, it is not divisible by 2. Since the given number is not divisible by both 2 and 3 therefore, it is not divisible by 6. Since, the given number is not divisible by both 2 and 3, it is not divisible by 6. Since, the given number is not divisible by both 2 and 3 hence, it is not divisible by 6.

Using divisibility tests, determine which of the following numbers are divisible by a b c d e We know that a number is divisible by 11 if the difference between the sum of the digits at odd places from the right and the sum of the digits at even places from the right of the number is either 0 or divisible by Hence, the given number is divisible by Hence, the given number is not divisible by Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3.

Hence, the required digits are 0 and 9. Write a digit in the blank space of each of the following numbers so that the numbers formed is divisible by Find the common factors of: a 20 and 28 b 15 and 25 c 35 and 50 d 56 and Solution: a Given numbers are : 20 and 28 Factors of 20 are 1, 2, 4, 5, 10, 20 Factors of 28 are 1, 2, 4, 7, 28 Hence, the common factors are 1, 2 and 4.

Find the common factors of: a 4, 8 and 12 b 5, 15 and 25 6 8 Solution: a Given numbers are: 4, 8 and 12 Factors of 4 are 1, 2, 4 Factors of 8 are 1, 2, 4, 8 Factors of 12 are 1, 2, 3, 4, 6, 12 Hence, the common factors are 1, 2 and 4. Write all the numbers less than which are common multiples of 3 and 4. Solution: Given numbers are 3 and 4. Multiples of 3 less than are: Hence, the common multiples of 3 and 4 less than are: 12, 24, 36, 48, 60, 72, 84 and Which of the following numbers are co-prime?

Hence, 18 and 35 are co-prime. Hence, they are co-prime. A number is divisible by both 5 and Byjus Class 8 Maths Chapter 6 Number By which other will that number be always divisible? Solution: If the number is divisible by both 5 and 12 this the number will also be divisible by 5 x 12 i.

A number is divisible by By what other will that number be divisible? Solution: Factors of 12 are 1, 2, 3, 4, 6, 12 Hence the number which is Byjus Class 6 Maths Chapter 3 Case divisible by 12, will also be divisible by its factors i. Which of the following statements are true? Here are two different factor trees for Write the missing numbers. Which factors are not included in the prime factorisation of a composite number?

Solution: 1 and the number itself are not included in the prime factorisation of a composite number. Write the greatest 4-digit number and express it in terms of its prime factors.

Write the smallest 5-digit number and express it in the form of its prime factors. Find all the prime factors of and arrange them in ascending order. Now state the relations, if any, between the two consecutive prime factors. The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples. Solution: Example 1: Take three consecutive numbers 20, 21 and Here 20 is divisible by 2 and 21 is divisible by 3.

Example 2: Take three consecutive numbers 30; 31 and Hence This is prime factorization. There is not a composite number in this process of factorization. In this factorization, 2 and 3 are prime numbers, but 9 is a composite number. Q10 Determine if is divisible by Test the divisibility of the number by 5 and 9]. As the sum of the digits of is divisible by 9, therefore. Since the number is divisible by 5 and 9 both, it is divisible by Q12 I am the smallest number, having four different prime factors.

Can you find me? Answer: Since it is the smallest number of such type, it will be the product of 4 smallest prime numbers. Q Find the HCF of the following: i 24 and 36 ii 15, 25 and 30 iii 8 and 12 iv 12, 16 and Answer: i 24 and Q1 Find the HCF of the following numbers : a 18, 48 b 30, 42 c 18, 60 d 27, 63 e 36, 84 f 34, g 70, , h 91, , 49 i 18, 54, 81 j 12, 45, Answer: a 18, Q2 What is the HCF of two consecutive a numbers?

Answer: a 1 e. Is the answer correct? If not, what is the correct HCF? Answer: No, the answer is not correct. Q1 Renu purchases two bags of fertilizer of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertilizer exact number of times. Hence the maximum value of weight which can measure the weight of the fertilizer exact number of times is 3. Q2 Three boys step off together from the same spot.

Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can cover the distance in complete steps? Q3 The length, breadth and height of a room are cm, cm and cm respectively.

Find the longest tape which can measure the three dimensions of the room exactly. Q4 Determine the smallest 3-digit number which is exactly divisible by 6, 8 and Hence, the smallest 3-digit number which is exactly divisible by 6, 8, and 12 is Q5 Determine the greatest 3-digit number exactly divisible by 8, 10 and Answer: CM of 8, 10 and Hence, the greatest 3-digit number exactly divisible by 8, 10, and 12 is Q6 The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and seconds respectively.

If they change simultaneously at 7 a. They will change together after every seconds i. Q7 Three tankers contain litres, litres and litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of the three containers exact number of times. Hence the maximum capacity of a container that can measure the diesel of the three containers the exact number of times is Q8 Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.

Answer: LCM of 6, 15, Q9 Find the smallest 4-digit number which is divisible by 18, 24 and Answer: LCM of 18, 24 and Therefore, the smallest 4-digit number which is divisible by 18, 24, and 32 is Is LCM the product of two numbers in each case?

Yes, it can be observed that in each case, the LCM of the given numbers is the product of these numbers. When two numbers are co-prime, their LCM is the product of those numbers. Also, in each case, LCM is a multiple of 3.

Q11 Find the Byjus Class 7 Maths Chapter 3 Vis LCM of the following numbers in which one number is the factor of the other. Yes, it can be observed that in each case, the LCM of the given numbers is the larger number.

When one number is a factor of the other number, their LCM will be the larger number. Chapters No. Chapters Name. Chapter - 1. Chapter - 2. Chapter - 3. Chapter - 4. Chapter - 5.

Chapter - 6. Chapter - 7. Chapter - 9. Chapter When you look back in life , this app would have played a huge role in laying the foundation of your career decisions. Found everything I wanted and it solved all of my queries for which I was searching a lot A must visit No need to find colleges in other sites, this is the best site in India to know about any colleges in India.

Updated on Aug 17, - p. Ask Mr AL Share. Column 1 Column 2 i 35 a Multiple of 8 ii 15 b Multiple of 7 iii 16 c Multiple of 70 iv 20 d Factor of 30 v 25 e Factor of 50 f Factor of 20 Answer: Column 1 Column 2 i 35 b Multiple of 7 ii 15 d Factor of 30 iii 16 a Multiple of 8 iv 20 d Factor of 20 v 25 e Factor of Answer: Prime Number having the same digit are: 17,71 37,73 and 79, Answer: Prime numbers less than 20 are : 2, 3, 5, 7, 11, 13, 17, 19 Composite numbers less than 20 are : 4, 6, 8, 9, 10, 12, 14, 15, 16, Answer: three pairs of prime numbers whose difference is 2 are : 3,5 41,43 and 71, Answer: Seven consecutive composite numbers less than so that there is no prime number between them are : Between 89 and 97, both of which are prime numbers, there are 7 composite numbers.

Answer: a prime number b Composite number c Prime number, Composite number d 2 e 4 f 2. Q2 Using divisibility tests, determine which of the following numbers are divisible by 4; by 8: a b c d e f g h i j Answer: A number with 3 or more digits is divisible by 4 if the number formed by its last two digits is divisible by 4.

Q3 Using divisibility tests, determine which of the following numbers are divisible by 6: a b c d e f g h i j Answer: a Since the last digit Of the number is 4, it is divisible by 2. Therefore, the largest number is 8. Therefore, the largest number is 9.

Since the last digit of is 0. Hence, they will change simultaneously at am. Latest Articles. Kendriya Vidyalaya Admission for Class 1 - Check importan Read More. View All Latest Articles. Explore Popular Degree, Branches and Courses. Browse by Degrees. Browse by Courses. Computer Science Engineering. Mechanical Engineering. Civil Engineering. Information Technology. Electrical Engineering.

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