The product of two number is 4,107. If the H.C.F of this numbers is 37, then the greater number is:

Question: The product of two number is 4,107. If the H.C.F of this numbers is 37, then the greater number is:

Solution:
Let the two numbers be 37a and 37b, since their H.C.F is 37.

So, gcd(a, b) = 1.
Given,
Product of the numbers = 4107

So,
37a × 37b = 4107
⇒ 1369 ab = 4107
⇒ ab = 4107 ÷ 1369
= 3

So, a × b = 3
Now the co-prime factor pair of 3 is: (1, 3)

So the two numbers are:
37 × 1 = 37
37 × 3 = 111

Therefore, the greater number is 111.