Question

Find the number of positive integers co-prime to
480 and less than it. Also find the sum of all those
numbers​

Answer 1

Answer:

If N is a number that can be written as ap .bq .cr …….., then, the number of co-primes of N, which are less than N, represented by ϕ (N) is,

N(1- 1/a ) (1- 1/b ) (1- 1/c )…………………

For e.g., if 48, is considered,

N= N=ap .bq .cr ……. i.e. 48=24. 31.

Hence, a=2, b=3, p=4, q=1.

ϕ (48) = 48(1- 1/2 ) (1- 1/3 )

= 48 x 1/2 x 1/3

=16