Question

The sum of two numbers is 204 and their HCF is 17. Find all the possible pairs of such numbers. Answer will be 119 but please explain with process ​

Answer 1

Answer:

Since the HCF is 17, the number must be of the form 17a and 17b, where a and b are prime to each other.

Given, 17a + 17b = 204

=> a + b = 12

The possible pairs of numbers whose sum is 12 are 1, 11; 2, 10; 3, 9; 4, 8; 5, 7; 6, 6

The only pairs of numbers which are prime to each other are 1, 11; 12, 10; 3, 9; 4, 8; 5, 7; 6, 6

Therefore, the required pairs are 17 × 1 = 17

and 17 × 11 = 187

and 17 × 5 = 85

and 17 × 7 = 119.