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How many integral divisors does the number 120 have?
- a)14
- b)16
- c)12
- d)20
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
How many integral divisors does the number 120 have?a)14b)16c)12d)20e)...
Step 1 of solving this GMAT Number Properties Question: Express the number in terms of its prime factors
120 = 23 * 3 * 5.
The three prime factors are 2, 3 and 5.
The powers of these prime factors are 3, 1 and 1 respectively.
The three prime factors are 2, 3 and 5.
The powers of these prime factors are 3, 1 and 1 respectively.
Step 2 of solving this GMAT Number Properties Question:Find the number of factors as follows
To find the number of factors / integral divisors that 120 has, increment the powers of each of the prime factors by 1 and then multiply them.
Number of factors = (3 + 1) * (1 + 1) * (1 + 1) = 4 * 2 * 2 =16
Choice B is the correct answer.
Most Upvoted Answer
How many integral divisors does the number 120 have?a)14b)16c)12d)20e)...
Solution:
To find the integral divisors of a number, we need to find all the positive integers that divide the number without leaving any remainder.
Prime Factorization of 120:
120 = 2^3 × 3 × 5
To find all the divisors of 120, we can use the prime factorization.
We can find all the divisors of 120 by choosing a combination of the prime factors 2, 3, and 5.
To find the number of divisors, we can use the following formula:
Number of divisors = (a+1) × (b+1) × (c+1) × …
where a, b, c, … are the powers of the prime factors in the prime factorization.
For 120, a=3, b=1, and c=1.
Therefore, the number of divisors of 120 = (3+1) × (1+1) × (1+1) = 4 × 2 × 2 = 16
Hence, the correct answer is option B, 16.
To find the integral divisors of a number, we need to find all the positive integers that divide the number without leaving any remainder.
Prime Factorization of 120:
120 = 2^3 × 3 × 5
To find all the divisors of 120, we can use the prime factorization.
We can find all the divisors of 120 by choosing a combination of the prime factors 2, 3, and 5.
To find the number of divisors, we can use the following formula:
Number of divisors = (a+1) × (b+1) × (c+1) × …
where a, b, c, … are the powers of the prime factors in the prime factorization.
For 120, a=3, b=1, and c=1.
Therefore, the number of divisors of 120 = (3+1) × (1+1) × (1+1) = 4 × 2 × 2 = 16
Hence, the correct answer is option B, 16.
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How many integral divisors does the number 120 have?a)14b)16c)12d)20e)None of theseCorrect answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many integral divisors does the number 120 have?a)14b)16c)12d)20e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many integral divisors does the number 120 have?a)14b)16c)12d)20e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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