Question

What is the smallest positive number that can be added to 55 so that the resulting number and 45 have 9 as their greatest common factor?

Answer 1

The smallest positive number is 8

Explanation:

let the smallest positive number = x

45 is a multiple of 9 ⇒ 9 x 5 = 45

the next multiple of 9 after 55 is 63

= 9 x 7

= 63

Thus, x + 55 = 63

x = 63 - 55

x = 8

The greatest common factor of 45 and 63 = 9

Therefore, the smallest positive number is 8