## RS Aggarwal Class 6 Math Second Chapter Factors And Multiples Exercise 2A Solution

## EXERCISE 2A

**1. Define:**

**(i) FACTOR:** *A factor of a number is an exact divisor of that number.*

**(ii) MULTIPLE:** *A number is said to be a multiple of any of its factors.*

Example- We know that 15= 1 x 15 and 15= 3 x 5.

This shows that each of the numbers 1, 3, 5, 15 are all factors of 15.

**2. Write down all the factors of**

(i) 20= 1,2,4,5,10,20.

(ii) 36= 1, 2, 3, 4, 6, 9, 12, 18, 36.

(iii) 60= 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

(iv) 75= 1, 3, 5, 15, 25, 75

**3. Write the first five multiple of each of the following numbers:**

(i) 17= 17, 34, 51, 68, 85

(ii) 23= 23, 46, 69, 92, 115

(iii) 65= 65, 130, 195, 260, 325

(iv) 70= 70, 140, 210, 280, 350

**4. Which of the following numbers are even and which are the odd?**

(i) 32= Even

(ii) 37= Odd

(iii) 50= Even

(iv) 58= Even

(v) 69= Odd

(vi) 144= Even

(vii) 321= Odd

(viii) 253= Odd

**5. What are Prime Numbers? Give ten examples.**

**Ans: ***Each of the numbers which have exactly two factors, namely, 1 and itself, is called a Prime Number.*

*Example- The numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc are all prime number.*

**6. Write all the prime numbers between **

(i) 10 and 40= 11, 13, 17, 19, 23, 29, 31, 37

(ii) 80 and 100= 83, 89, 97

(iii) 40 and 80= 41, 43, 47, 53, 59, 61, 67, 71, 73, 79

(iv) 30 and 40= 31, 37

**7. (i) Write the smallest prime number.**

*The smallest prime number is 2.*

**(ii) List all even prime numbers.**

*The even prime numbers are 2.*

**(iii) Write the smallest odd prime number.**

*The smallest odd prime number is 3.*

**8. Find which of the following numbers are prime:**

(i) 87

(ii) 89

(iii) 63

(iv) 91

**Ans:** *89 is a prime number.*

**9. Make a list of seven consecutive numbers, none of which is prime.**

**Ans:** The consecutive numbers are 90 , 91, 92, 93, 94, 95, 96.

**10. (i) Is there any counting number having no factor at all?**

**Ans:** No.

**(ii) Find all the numbers having exactly one factor.**

**Ans:** 1.

**(iii) Find numbers between 1 and 100 having exactly three factors.**

** Ans:** 4, 9, 25, 49.

**11. What are composite numbers? Can a composite number be odd? If yes, write the smallest odd composite number.**

**Ans:** COMPOSITE NUMBERS: *Numbers having more than two factors are known as composite numbers. *

*Yes a composite number can odd. The smallest odd composite number is 9.*

**12. What are twin primes? Write all the pairs of twin primes between 50 and 100.**

**Ans:** TWIN PRIMES: *Two consecutive odd prime numbers are known as twin primes.*

*(59, 61), (71, 73) are the pairs of twin primes between 50 and 100.*

**13. What are co-primes? Give examples of five pairs of five pairs of co-primes. Are co-primes always primes? If no, illustrate your answer by an example.**

**Ans:** CO-PRIMES: *Two numbers are said to be co-primes if they do not have a common factor other than 1.*

*No, co-primes are not be always primes.*

*For example 6, 7 are co-primes, while 6 is not a prime number.*

**14. Express each of the following umbers as the sum of two odd primes:**

(i) 36= 7+ 29

(ii) 42= 5+ 37

(iii) 84= 17+ 67

(iv) 98= 79+ 19

**15. Express each of the following odd numbers as the sum of three odd prime numbers:**

(i) 31= 5+ 7+ 19

(ii) 35= 5 + 7+ 23

(iii) 49= 3 + 5 41

(iv) 63= 7+ 13+ 43

**16. Express each of the following numbers as the sum of twin primes:**

(i) 36= 17+ 19

(ii) 84= 41+ 43

(iii) 120= 59+ 61

(iv) 144= 71+ 73

**17. Which of the following statements are true?**

(i) 1 is smallest prime number.

(ii) If a number is prime, it must be odd.

(iii) The sum of two prime numbers is always a prime number.

(iv) If two numbers are co-primes, at least one of them must be a prime number.

**Ans:** None.

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