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The Greatest Common Factor (GCF) of 48 and 72 is

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Bunuel
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The Greatest Common Factor (GCF) of 48 and 72 is [#permalink] New post   23 Oct 2018, 21:31
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A
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D
E

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Question Stats:

87% (00:49) correct 13% (00:56) wrong based on 148 sessions
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The Greatest Common Factor (GCF) of 48 and 72 is

A. 4
B. 6
C. 12
D. 24
E. 48
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D
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Re: The Greatest Common Factor (GCF) of 48 and 72 is [#permalink] New post   23 Oct 2018, 21:37
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Bunuel wrote:
The Greatest Common Factor (GCF) of 48 and 72 is

A. 4
B. 6
C. 12
D. 24
E. 48


48 = 24*2
72 = 24*3

there is no GCD of 2 and 3 except 1 therefore GCF of 48 and 72 = 24

Answer: Option D
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Re: The Greatest Common Factor (GCF) of 48 and 72 is [#permalink] New post   23 Oct 2018, 21:50
48 = \(3\) * \(2^4\)
72 = \(3^2\) * \(2^3\)

From both the numbers \(3\) * \(2^3\) is common for both.

So GCD is \(3\) * \(2^3\) = \(24\)
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Re: The Greatest Common Factor (GCF) of 48 and 72 is [#permalink] New post   23 Oct 2018, 23:56
Bunuel wrote:
The Greatest Common Factor (GCF) of 48 and 72 is

A. 4
B. 6
C. 12
D. 24
E. 48


24*2 = 48
24*3 = 72

Hence, Answer must be (D) 24
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Re: The Greatest Common Factor (GCF) of 48 and 72 is [#permalink] New post   26 Apr 2020, 18:04
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Bunuel wrote:
The Greatest Common Factor (GCF) of 48 and 72 is

A. 4
B. 6
C. 12
D. 24
E. 48


48 = (2)(2)(2)(2)(3)
72 = (2)(2)(2)(3)(3)

Prime factors in common = (2)(2)(2)(3) = 24

Answer: D

Cheers,
Brent
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The Greatest Common Factor (GCF) of 48 and 72 is [#permalink] New post   27 Oct 2022, 12:25
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We need to find The greatest common factor (GCF) of 48 and 72

Lets solve it using two methods

Method 1: Prime Factorization

48 = 3*16 = \(2^4 * 3^1\)
72 = 8*9 = \(2^3 * 3^2\)

To find the GCF take all the common terms and take their lowest power in all of the above.

=> GCF(48,72) = \(2^3 * 3^1\) = 24

So, Answer will be D

Method 2: Common Division Method

4 | 48, 72
-----------
6 | 12 , 18
------------
__| 2, 3

=> GCF = Product of Common factors = 4*6 = 24

So, Answer will be D
Hope it helps!

To learn more about LCM and GCD watch the following videos



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Re: The Greatest Common Factor (GCF) of 48 and 72 is [#permalink] New post   28 Oct 2022, 05:59
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Bunuel wrote:
The Greatest Common Factor (GCF) of 48 and 72 is

A. 4
B. 6
C. 12
D. 24
E. 48


The largest factor of both 48 and 72 is 24, since 48/24 = 2 and 72/24 = 3.

Answer: D
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Re: The Greatest Common Factor (GCF) of 48 and 72 is [#permalink]
28 Oct 2022, 05:59
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