GMAT Exam > GMAT Questions > How many integral divisors does the number 12...
Start Learning for Free
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: 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: 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.
Key Takeaway
How to find the number of factors of a number? Method: Prime Factorization
Let the number be 'n'.
Step 1: Prime factorize 'n'. Let n = ap * bq, where 'a' and 'b' are the only prime factors of 'n'.
Step 2: Number of factors equals product of powers of primes incremented by 1.
i.e., number of factors = (p + 1)(q + 1)
How to find the number of factors of a number? Method: Prime Factorization
Let the number be 'n'.
Step 1: Prime factorize 'n'. Let n = ap * bq, where 'a' and 'b' are the only prime factors of 'n'.
Step 2: Number of factors equals product of powers of primes incremented by 1.
i.e., number of factors = (p + 1)(q + 1)
Most Upvoted Answer
How many integral divisors does the number 120 have?a)14b)16c)12d)20e)...
Understanding the Problem
To find the number of integral divisors of the number 120, we first need to determine its prime factorization.
Prime Factorization of 120
1. Start by dividing 120 by the smallest prime number, which is 2.
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
2. Now, 15 is not divisible by 2. Move to the next prime number, which is 3.
- 15 ÷ 3 = 5
3. Finally, 5 is a prime number itself.
Hence, the prime factorization of 120 is:
- 120 = 2^3 × 3^1 × 5^1
Calculating the Number of Divisors
The formula to find the number of integral divisors from the prime factorization is:
- If a number is expressed as p1^e1 × p2^e2 × ... × pk^ek, then the number of divisors (d) is given by:
d = (e1 + 1)(e2 + 1)...(ek + 1)
For 120:
- e1 = 3 (for 2)
- e2 = 1 (for 3)
- e3 = 1 (for 5)
Now, applying the formula:
- Number of divisors = (3 + 1)(1 + 1)(1 + 1)
Calculation
- Number of divisors = 4 × 2 × 2 = 16
Conclusion
Thus, the number of integral divisors of 120 is 16, confirming that the correct answer is option 'B'.
To find the number of integral divisors of the number 120, we first need to determine its prime factorization.
Prime Factorization of 120
1. Start by dividing 120 by the smallest prime number, which is 2.
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
2. Now, 15 is not divisible by 2. Move to the next prime number, which is 3.
- 15 ÷ 3 = 5
3. Finally, 5 is a prime number itself.
Hence, the prime factorization of 120 is:
- 120 = 2^3 × 3^1 × 5^1
Calculating the Number of Divisors
The formula to find the number of integral divisors from the prime factorization is:
- If a number is expressed as p1^e1 × p2^e2 × ... × pk^ek, then the number of divisors (d) is given by:
d = (e1 + 1)(e2 + 1)...(ek + 1)
For 120:
- e1 = 3 (for 2)
- e2 = 1 (for 3)
- e3 = 1 (for 5)
Now, applying the formula:
- Number of divisors = (3 + 1)(1 + 1)(1 + 1)
Calculation
- Number of divisors = 4 × 2 × 2 = 16
Conclusion
Thus, the number of integral divisors of 120 is 16, confirming that the correct answer is option 'B'.
|
Explore Courses for GMAT exam
|
|
Top Courses for GMATView all
Question Description
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?.
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?.
Solutions 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? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily