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How many Factors of 240 are divisible by 12?

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How many Factors of 240 are divisible by 12?  [#permalink]

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New post 24 Jan 2020, 04:16
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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)
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Re: How many Factors of 240 are divisible by 12?  [#permalink]

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New post 24 Jan 2020, 04:43
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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

Answer (1)
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Re: How many Factors of 240 are divisible by 12?   [#permalink] 24 Jan 2020, 04:43
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