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

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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