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# How many Factors of 240 are divisible by 12?

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Senior Manager
Joined: 09 Jan 2017
Posts: 350
Location: India
How many Factors of 240 are divisible by 12?  [#permalink]

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24 Jan 2020, 04:16
3
00:00

Difficulty:

45% (medium)

Question Stats:

47% (01:29) correct 53% (01:34) wrong based on 15 sessions

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How many Factors of 240 are divisible by 12?
1>6
2>4
3>5
4>8
5>7

Source: - Time (CAT)
GMAT Tutor
Status: Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
Joined: 26 Jun 2014
Posts: 107
GMAT 1: 740 Q51 V39
Re: How many Factors of 240 are divisible by 12?  [#permalink]

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24 Jan 2020, 04:43
4
Question:
How many Factors of 240 are divisible by 12?

Solution:

$$12 = 2^2 * 3$$

$$240 = 2^4 * 3 * 5$$

We need to determine the factors of 240 that are divisible by 12

240 = 12 x 20

Thus, if we can determine the factors of 20, then 12 multiplied with each of those factors would result in those factors of 240 which are divisible by 12

Thus, in essence, we simply need to determine the number of factors of 20

$$20 = 2^2 * 5^1$$

Thus, the number of factors is a combination of $$(2^0, 2^1, 2^2)$$ and $$(5^0, 5^1)$$

Thus, number of factors of 20 = 3 * 2 = 6

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Sujoy Kumar Datta
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Re: How many Factors of 240 are divisible by 12?   [#permalink] 24 Jan 2020, 04:43
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