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The product of two numbers is 2160 and their HCF is 12. Number of such possible pairs is
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The product of two numbers is 2160 and their HCF is 12. Number of such...
Given information:
The product of two numbers is 2160 and their HCF is 12.
Solution:
Step 1: Prime factorization of 2160
2160 = 2^4 * 3^3 * 5
Step 2: Pairing the factors to find the numbers
Since the HCF is 12, we need to pair the common factors of the two numbers.
Possible pairs of numbers are:
1. 12 * 180 = 2160
2. 24 * 90 = 2160
Therefore, there are 2 possible pairs of numbers that satisfy the given conditions.
Final Answer:
b) 2
The product of two numbers is 2160 and their HCF is 12.
Solution:
Step 1: Prime factorization of 2160
2160 = 2^4 * 3^3 * 5
Step 2: Pairing the factors to find the numbers
Since the HCF is 12, we need to pair the common factors of the two numbers.
Possible pairs of numbers are:
1. 12 * 180 = 2160
2. 24 * 90 = 2160
Therefore, there are 2 possible pairs of numbers that satisfy the given conditions.
Final Answer:
b) 2
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Community Answer
The product of two numbers is 2160 and their HCF is 12. Number of such...
HCF = 12
Numbers = 12x and 12y
where x and y are prime to each other.
∴ 12x × 12y = 2160
= 15 = 3 × 5, 1 × 15
Possible pairs = (36, 60) and (12, 180)
Hence , Number of such possible pairs is 2.
Numbers = 12x and 12y
where x and y are prime to each other.
∴ 12x × 12y = 2160
= 15 = 3 × 5, 1 × 15
Possible pairs = (36, 60) and (12, 180)
Hence , Number of such possible pairs is 2.
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The product of two numbers is 2160 and their HCF is 12. Number of such possible pairs isa)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?
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