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Number systems
February 09, 2004
How many integral divisors does the number 120 have?
| (A) | 14 |
| (B) | 16 |
| (C) | 12 |
| (D) | 20 |
| (E) | None of these |
Correct Answer (B) Choice (16)
Solution:
Express the number 120 as a product of powers of prime factors.
In this case, 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.
To find the number of factors / integral divisors that 120 has, increment the powers of the prime factors by 1 and then multiply them.
In this case, (3+1) * (1 + 1) * (1 + 1) = 4 * 2 *2 = 16.
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