Solution of all questions of RS Aggarwal Class 6 Chapter 2 Exercise 2A Solution (Factors and Multiples).
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Question 1: Define (i) factor (ii) multiple. Give five examples of each.
Factor: A factor of a number is an exact divisor of that number.
For example: factors of 20 is 1, 2, 4, 5, 10 and 20
Multiple: A number is said to be multiple of any of its factors.
For Example: Multiple of 2 is 2, 4, 6, 8 and 10.
Question 2: Write down all the factors of
(i) 20
Factors of 20 is 1, 2, 4, 5, 10 and 20
(ii) 36
Factors of 36 is 1, 2, 3, 4, 6, 9, 12, 18 and 36
(iii) 60
Factors of 60 is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60
(iv) 75
Factors of 75 is 1, 3, 5, 15, 25 and 75
Question 3: Write the first five multiples of each of the following numbers:
(i) 17
Multiple of 17 is, 17, 34, 51, 68 and 85
(ii) 23
Multiple of 23 is, 23, 46, 69, 92 and 115
(iii) 65
Multiple of 65 is 65, 130, 195, 260 and 325
(iv) 70
Multiple of 70 is 70, 140, 210, 280 and 350
Question 4: Which of the following numbers are even and which are odd?
(i) 32 (ii) 70 (iii) 50 (iv) 58 (v) 69 (vi) 144 (vii) 321 (viii) 253
The number which is divisible by 2 is called even number and the number which is not divisible by 2 is called odd number.
Even number is 32, 70, 50, 58 and 144
Odd number 69, 321 and 253
Question 5: Which are prime numbers? Give ten examples.
The number which divisible by 1 and itself, is called prime number.
For example: 2, 3, 5, 7 11, 13, 17, 19, 23 and 29 are prime numbers.
Question 6: Write all the prime numbers between.
(i) 10 and 40
Prime number between 10 and 40 is 11, 13, 17, 19, 23, 29, 31 and 37
(ii) 80 and 100
Prime number between 80 and 100 is 83, 89 and 97
(iii) 40 and 80
Prime number between 40 and 80 is 41, 43, 47, 53, 59, 61, 67, 71, 73 and 79
(iv) 30 and 40
Prime number between 30 and 40 is 31 and 37
Question 7:
(i) Write the smallest prime number.
Smallest prime number is 2.
(ii) List all even prime numbers.
All even prime number is 2.
(iii) Write the smallest odd prime number.
Smallest odd prime number is 3.
Question 8: Find which of the following numbers are primes.
(i) 87 (ii) 89 (iii) 63 (iv) 91
In given numbers 89 is prime number.
Question 9: Make a list of seven consecutive numbers, none of which is prime.
List of seven number is 90, 91, 92, 93, 94, 95 and 96
Question 10:
(i) Is there any counting number having no factor at all .
No
(ii) Find all the numbers having exactly one factor
The number which have exactly one factor is 1.
(iii) Find numbers between 1 and 100 having exactly three factors.
Number between 1 and 100 having three factors are 4, 9, 25 and 49
Question 11:
What are composite numbers? Can a composite numbers be odd? If yes, write the smallest odd composite number.
All the number except 1 and prime number is called composite number. Yes the composite number be odd number, the smallest odd composite number is 9.
Question 12:
What are twin primes? Write all the pairs of twin primes between 50 and 100.
Two consecutive odd prime numbers are known as twin prime numbers. Twin primes pairs between 50 and 100 are (59, 61) and (71, 73).
Question 13:
What are co-primes? Give examples of five pairs of co-primes. Are co-primes always primes? If no, illustrate your answer by an examples.
Two number is said to be co- prime numbers, if they do not have common factor other than 1. Example are (2, 3), (7, 9), (11, 14), (5, 9) and (4, 9).
No, co – prime are not always prime, for example (11, 14) are co-prime but 14 is not prime.
Question 14:
Express each of the following numbers as the sum of two odd primes:
(i) 36
36 = 17 +19
(ii) 42
42 = 23 + 19
(iii) 84
84 = 41 + 43
(iv) 98
98 = 31 + 67
Question 15:
Express each of the following odd numbers as the sum of three odd prime numbers:
(i) 31
31 = 7 + 11 + 13
(iii) 49
49 = 3 + 5 + 41
(iv) 63
63 = 7 + 13 + 43
Question 16:
Express each of the following numbers as the sum of twin primes:
(i) 36
36 = 17 + 19
(ii) 84
84 = 41 + 43
(iii) 120
120 = 59 + 61
(iv) 144
144 = 71 + 73
Question 17:
Which of the following statements are true?
(i)1 is the smallest prime number.
False
(ii) If a numbers is prime, it must be odd.
False
(iii)The sum of two prime numbers is always a prime number.
False
(iv) If two numbers are co-prime, at last one of them must be a prime number.
False
Therefore all statements are false.