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The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
- a)101
- b)107
- c)111
- d)185
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The product of two numbers is 4107. If the H.C.F. of these numbers is ...
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.
Most Upvoted Answer
The product of two numbers is 4107. If the H.C.F. of these numbers is ...
Given: The product of two numbers is 4107 and the H.C.F. of these numbers is 37.
To find: The greater number.
Approach:
We know that product of two numbers = LCM × HCF
Steps:
1. Find the LCM of the two numbers using the formula:
LCM × HCF = Product of the two numbers
LCM × 37 = 4107
LCM = 111
2. We can write the two numbers as:
37a and 37b (where a and b are co-primes)
Product of the two numbers = 37a × 37b = 13749ab
Given, product of the two numbers = 4107
Therefore, ab = 111
3. We need to find the greater number, which is 37 times either a or b.
37a = 37 × a
37b = 37 × b
Since a and b are co-primes, only one of them can be a multiple of 37.
If a is a multiple of 37, then b = 3.
If b is a multiple of 37, then a = 3.
Therefore, the greater number is 37b = 37 × 3 = 111.
Hence, the correct answer is option C) 111.
To find: The greater number.
Approach:
We know that product of two numbers = LCM × HCF
Steps:
1. Find the LCM of the two numbers using the formula:
LCM × HCF = Product of the two numbers
LCM × 37 = 4107
LCM = 111
2. We can write the two numbers as:
37a and 37b (where a and b are co-primes)
Product of the two numbers = 37a × 37b = 13749ab
Given, product of the two numbers = 4107
Therefore, ab = 111
3. We need to find the greater number, which is 37 times either a or b.
37a = 37 × a
37b = 37 × b
Since a and b are co-primes, only one of them can be a multiple of 37.
If a is a multiple of 37, then b = 3.
If b is a multiple of 37, then a = 3.
Therefore, the greater number is 37b = 37 × 3 = 111.
Hence, the correct answer is option C) 111.
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The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:a)101b)107c)111d)185Correct answer is option 'C'. Can you explain this answer?
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The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:a)101b)107c)111d)185Correct answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:a)101b)107c)111d)185Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:a)101b)107c)111d)185Correct answer is option 'C'. Can you explain this answer?.
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:a)101b)107c)111d)185Correct answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:a)101b)107c)111d)185Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:a)101b)107c)111d)185Correct answer is option 'C'. Can you explain this answer?.
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