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If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following?
- a)8
- b)12
- c)18
- d)24
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If positive integer n is divisible by both 4 and 21, then n must be di...
Explanation:
Divisibility Rules:
- For a number to be divisible by 4, the last two digits of the number must be divisible by 4.
- For a number to be divisible by 21, it must be divisible by both 3 and 7.
Analysis:
- Since n is divisible by 4 and 21, it must be divisible by 4 and by 21.
- This means n must have factors of both 4 and 21.
Finding the Common Factors:
- The prime factorization of 4 is 2^2 and the prime factorization of 21 is 3*7.
- The common factors between 4 and 21 are 1 and 2.
Identifying the Correct Answer:
- The only answer choice that includes the common factor of 2 is 12.
- Therefore, if n is divisible by both 4 and 21, it must also be divisible by 12.
Conclusion:
- The correct answer is option B) 12.
Divisibility Rules:
- For a number to be divisible by 4, the last two digits of the number must be divisible by 4.
- For a number to be divisible by 21, it must be divisible by both 3 and 7.
Analysis:
- Since n is divisible by 4 and 21, it must be divisible by 4 and by 21.
- This means n must have factors of both 4 and 21.
Finding the Common Factors:
- The prime factorization of 4 is 2^2 and the prime factorization of 21 is 3*7.
- The common factors between 4 and 21 are 1 and 2.
Identifying the Correct Answer:
- The only answer choice that includes the common factor of 2 is 12.
- Therefore, if n is divisible by both 4 and 21, it must also be divisible by 12.
Conclusion:
- The correct answer is option B) 12.
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If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following?a)8b)12c)18d)24Correct answer is option 'B'. Can you explain this answer?
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