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The H.C.F and the product of two numbers are 15 and 6300 respectively. The number of possible pairs of numbers is:
- a)2
- b)3
- c)4
- d)7
Correct answer is option 'A'. Can you explain this answer?
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The H.C.F and the product of two numbers are 15 and 6300 respectively....
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The H.C.F and the product of two numbers are 15 and 6300 respectively....
The H.C.F and the product of two numbers
Given:
- H.C.F (Highest Common Factor) of two numbers = 15
- Product of the two numbers = 6300
To find the number of possible pairs of numbers, we need to find the factors of 6300 and check which pairs have a H.C.F of 15.
Factors of 6300
To find the factors of 6300, we can prime factorize it.
Prime factorization of 6300:
6300 = 2 * 3 * 3 * 5 * 5 * 7
Finding the factors
To find the factors, we can start with the smallest prime factor (2) and systematically increase it to the next prime factor (3, 5, 7) while keeping track of the number of times each prime factor is used.
Factors of 6300:
2^0 * 3^0 * 5^0 * 7^0 = 1 (no prime factors used)
2^1 * 3^0 * 5^0 * 7^0 = 2
2^0 * 3^1 * 5^0 * 7^0 = 3
2^2 * 3^0 * 5^0 * 7^0 = 4
2^1 * 3^1 * 5^0 * 7^0 = 6
2^0 * 3^0 * 5^1 * 7^0 = 5
2^3 * 3^0 * 5^0 * 7^0 = 8
2^2 * 3^1 * 5^0 * 7^0 = 12
2^1 * 3^2 * 5^0 * 7^0 = 18
2^0 * 3^0 * 5^0 * 7^1 = 7
2^4 * 3^0 * 5^0 * 7^0 = 16
2^3 * 3^1 * 5^0 * 7^0 = 24
2^2 * 3^0 * 5^1 * 7^0 = 20
2^1 * 3^1 * 5^1 * 7^0 = 30
2^0 * 3^2 * 5^0 * 7^0 = 9
2^5 * 3^0 * 5^0 * 7^0 = 32
2^4 * 3^1 * 5^0 * 7^0 = 48
2^3 * 3^2 * 5^0 * 7^0 = 72
2^2 * 3^0 * 5^1 * 7^0 = 40
2^1 * 3^1 * 5^1 * 7^0 = 60
2^0 * 3^3 * 5^0 * 7^0 = 27
2^6 * 3^0 * 5^0 * 7^0 = 64
2^5 * 3^1 * 5^0 * 7^0
Given:
- H.C.F (Highest Common Factor) of two numbers = 15
- Product of the two numbers = 6300
To find the number of possible pairs of numbers, we need to find the factors of 6300 and check which pairs have a H.C.F of 15.
Factors of 6300
To find the factors of 6300, we can prime factorize it.
Prime factorization of 6300:
6300 = 2 * 3 * 3 * 5 * 5 * 7
Finding the factors
To find the factors, we can start with the smallest prime factor (2) and systematically increase it to the next prime factor (3, 5, 7) while keeping track of the number of times each prime factor is used.
Factors of 6300:
2^0 * 3^0 * 5^0 * 7^0 = 1 (no prime factors used)
2^1 * 3^0 * 5^0 * 7^0 = 2
2^0 * 3^1 * 5^0 * 7^0 = 3
2^2 * 3^0 * 5^0 * 7^0 = 4
2^1 * 3^1 * 5^0 * 7^0 = 6
2^0 * 3^0 * 5^1 * 7^0 = 5
2^3 * 3^0 * 5^0 * 7^0 = 8
2^2 * 3^1 * 5^0 * 7^0 = 12
2^1 * 3^2 * 5^0 * 7^0 = 18
2^0 * 3^0 * 5^0 * 7^1 = 7
2^4 * 3^0 * 5^0 * 7^0 = 16
2^3 * 3^1 * 5^0 * 7^0 = 24
2^2 * 3^0 * 5^1 * 7^0 = 20
2^1 * 3^1 * 5^1 * 7^0 = 30
2^0 * 3^2 * 5^0 * 7^0 = 9
2^5 * 3^0 * 5^0 * 7^0 = 32
2^4 * 3^1 * 5^0 * 7^0 = 48
2^3 * 3^2 * 5^0 * 7^0 = 72
2^2 * 3^0 * 5^1 * 7^0 = 40
2^1 * 3^1 * 5^1 * 7^0 = 60
2^0 * 3^3 * 5^0 * 7^0 = 27
2^6 * 3^0 * 5^0 * 7^0 = 64
2^5 * 3^1 * 5^0 * 7^0
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The H.C.F and the product of two numbers are 15 and 6300 respectively. The number of possible pairs of numbers is:a)2b)3c)4d)7Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The H.C.F and the product of two numbers are 15 and 6300 respectively. The number of possible pairs of numbers is:a)2b)3c)4d)7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The H.C.F and the product of two numbers are 15 and 6300 respectively. The number of possible pairs of numbers is:a)2b)3c)4d)7Correct answer is option 'A'. Can you explain this answer?.
The H.C.F and the product of two numbers are 15 and 6300 respectively. The number of possible pairs of numbers is:a)2b)3c)4d)7Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The H.C.F and the product of two numbers are 15 and 6300 respectively. The number of possible pairs of numbers is:a)2b)3c)4d)7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The H.C.F and the product of two numbers are 15 and 6300 respectively. The number of possible pairs of numbers is:a)2b)3c)4d)7Correct answer is option 'A'. Can you explain this answer?.
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