Three pairwise coprime numbers have ab = 551 and bc = 1073. Find a + b + c.

Given data

• a, b, c are pairwise coprime
• a·b = 551
• b·c = 1073

Concept / Approach

• If a, b, c are pairwise coprime, then b = gcd(a·b, b·c).
• Once b is found, a = 551 / b and c = 1073 / b.

Step-by-step calculation

gcd(551, 1073):1073 − 551 = 522551 − 522 = 29522 ÷ 29 = 18 remainder 0 ⇒ gcd = 29Thus b = 29a = 551 ÷ 29 = 19c = 1073 ÷ 29 = 37Sum = 19 + 29 + 37 = 85

Verification

Pairwise gcds: gcd(19,29)=1, gcd(29,37)=1, gcd(19,37)=1.

Common pitfalls

• Assuming b is a common prime factor without checking gcd.

Final Answer

a + b + c = 85.