Question

How many numbers between 1 to 72, do NOT have any common factor with 72
​

Answer 1

Answer:

20

Explanation:

U JUST NEED TO FIND THE PRIME NO.

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71

Answer 2

23 Numbers  1 to 72 do not have any common factors to 72 ( considering prime factors)

Given :   numbers 1 to 72

To Find : How many numbers 1 to 72 do not have any common factors to 72

Solution:

Factors of 72  = 1 , 2 , 3 , 4 , 6 , 8 , 9  , 12 , 18 , 24 , 36 , 72

All numbers have 1 as a common factor

Hence all 72 numbers  have common factors to 72

Answer is  0  numbers do not have any common factors to 72

But if Question is Prime factors

Now numbers which do not have any factor from

1 , 2 , 3 , 4 , 6 , 8 , 9  , 12 , 18 , 24 , 36 , 72

Prime factors of 72 = 2 , 3  

( simply all the prime factors except 2 , 3  and product of those prime factors )

5 , 7 , 11 , 13 , 17 , 19 , 23 , 25 , 29 , 31 , 35 , 37 , 41 , 43 , 47 , 49 , 53 , 55 , 59 , 61 , 65 , 67 , 71

There are 23 numbers  1 to 72  which do not have any common factors to 72

35 , 55 , 65  are not prime numbers but do not have any common factors to 72

Hence correct answer is 23 Numbers

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