Question

How many numbers up to 100 are co-prime to 19 and how?Please explain.

Answer 1

Answer:

The number of co-prime numbers to 19 from 1 to 100 is 95.

To find:

The number of co-prime numbers to 19 exist between 1 and 100  

Solution:

19 is a prime number.  

Factors of 19 up to 100 are 19, 38, 57, 76, 95.

So excluding these 5 numbers, all the other numbers are co-prime to 19.

∴ No. of numbers less than 100 that are co-prime to 19

= Total numbers between 1 and 100 – Number of factors of 19 from 1 to 100.

= 100 -5 = 95.

Thus, there are 95 co-prime numbers to 19 exists between 1 and 100.