The product of two numbers is 4107. If their H.C.F. is 37, find the greater number.

Given data

• Product of two numbers = 4107
• H.C.F. (gcd) of the two numbers = 37

Concept / Approach

• If HCF = h, then numbers can be written as h·x and h·y with gcd(x, y) = 1.
• Then product = h^2 · x · y ⇒ x · y = product / h^2.

Step-by-step calculation

h = 37 ⇒ h^2 = 37^2 = 1369x · y = 4107 ÷ 1369 = 3Coprime factor pairs of 3 are (1, 3)Numbers are 37·1 = 37 and 37·3 = 111

Verification

37 × 111 = 4107 and gcd(37, 111) = 37.

Common pitfalls

• Forgetting to divide the product by h^2 (not just by h).

Final Answer

Greater number = 111.