Discussion
The product of two numbers is 4,107 and their HCF is 37. What is the larger number?
Answer: C
Correct answer: 111
If the HCF is 37, both numbers are multiples of it, so write them as \( 37a \) and \( 37b \) where \( a \) and \( b \) are co-prime - they can share no further factor, or the HCF would be larger. Their product is \[ 37a \times 37b = 1369ab = 4107 \;\Rightarrow\; ab = 3. \] The only co-prime pair with product 3 is \( 1 \) and \( 3 \), so the numbers are \( 37 \times 1 = 37 \) and \( 37 \times 3 = 111 \). The larger is 111. Checking: \( 37 \times 111 = 4107 \) and \( \text{HCF}(37, 111) = 37 \). The co-primality requirement is what makes the method work and is the step usually forgotten. Had \( ab \) been 12, for instance, the admissible pairs would be only \( 1 \times 12 \) and \( 3 \times 4 \) - not \( 2 \times 6 \), since 2 and 6 share a factor.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development