The larger of two numbers — Number System Aptitude Question
The larger of two numbers: The product of two numbers is 4107 and their HCF is 37. What is the larger number? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
The product of two numbers is 4107 and their HCF is 37. What is the larger number?
Options
- 37
- 74
- 111
- 148
Show the answer and the worked solution
Correct answer: C. 111
Worked solution
- Let the numbers be 37a and 37b with a and b coprime.
- 37a × 37b = 4107 → 1369ab = 4107 → ab = 3.
- Coprime pair: a = 1, b = 3, so the numbers are 37 and 111.
- The larger is 111.
Answer: 111.
The idea
Pull the HCF out of both numbers and the leftovers must be coprime. That coprimality is what makes the factor pair unique — without it, ab = 3 would have other splits.
Shortcut. 4107 is odd, so neither number is even — 74 and 148 are out. Of 37 and 111 the larger is 111, and 37 × 111 = 4107 confirms it.
Common trap. 37 — the HCF itself, which here is the smaller of the two numbers; the question asks for the larger.