This GMAT Sample Math question is a Number Properties problem solving question and the concept covered is finding the number of factors or integral divisors of a number. A GMAT 650 to 700 level practice question.

Question 6: How many integral divisors does the number 120 have?

- 14
- 16
- 12
- 20
- None of these

@ INR

120 = 2^{3} * 3 * 5.

The three prime factors are 2, 3 and 5.

The powers of these prime factors are 3, 1 and 1 respectively.

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

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 = a^{p} * b^{q}, 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)

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2. Number Properties | Rational & Irrational Numbers

3. GMAT Number Properties | Indices & Rule of Exponents

4. Number Systems | Surds & Conjugates

5. Number Properties | Tests of divisibility

6. Number Properties | How to check whether a number is prime?

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8. GMAT Number Theory | Prime factorization | Properties of squares & cubes

9. Number Properties | What is HCF? | How to find HCF?

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12. Number Properties | When to use LCM and HCF?

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14. Number Theory | Number of ways to express as a product of 2 factors

15. Number Theory | Sum of all factors of a number

16. Number Theory | Product of all factors of a number

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18. Number Theory | Remainder of dividing x^{n} by 'd'

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20. Number Theory | Highest power of a prime that divides factorial of 'n'

21. Number Theory | Highest power of a composite number that divides factorial of 'n'

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