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How many of the factors of 42 are divisible by 3 ?

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Bunuel
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How many of the factors of 42 are divisible by 3 ? [#permalink] New post   06 Nov 2018, 00:14
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How many of the factors of 42 are divisible by 3 ?

A. 2
B. 3
C. 4
D. 6
E. 8
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C
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Re: How many of the factors of 42 are divisible by 3 ? [#permalink] New post   06 Nov 2018, 00:56
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Bunuel wrote:
How many of the factors of 42 are divisible by 3 ?

A. 2
B. 3
C. 4
D. 6
E. 8



Factors of 42 :

1 * 42
2 * 21
3*14
6*7


Among them only 42 , 21 , 6 , 3 are divisible by 3.

The best answer is C.
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Re: How many of the factors of 42 are divisible by 3 ? [#permalink] New post   06 Nov 2018, 01:01
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Factor of 42: 2^1 *3^1 * 7^1 (total 8 factor)
1,2,3,6,7,14,21, and 42

Divisible by 3:
3,6,21,and 42
total:-4

Answer: C
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Re: How many of the factors of 42 are divisible by 3 ? [#permalink] New post   01 Jul 2019, 17:48
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Bunuel wrote:
How many of the factors of 42 are divisible by 3 ?

A. 2
B. 3
C. 4
D. 6
E. 8


42 = 3 x 2 x 7

Thus, 3, 3 x 2, 3 x 7, and 3 x 2 x 7, are all divisible by 3.

Answer: C
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Re: How many of the factors of 42 are divisible by 3 ? [#permalink] New post   23 Nov 2018, 04:00
Does anyone know a shortcut to derive at "4" using the prime factorization? Or do we actually have to write down all the factors and just do the prime factorization to double-check that we have found all possible factors?
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Re: How many of the factors of 42 are divisible by 3 ? [#permalink] New post   23 Nov 2018, 04:24
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Method i used to drive at the correct answer is following

prime Factorization of 42 = 2^1 * 3^1 * 7^1

Now any factor of 42 will be divisible by 3 when it has 3 as its prime factor , means any factor of 42, should have power of 3 as 1 and 2 and 7 can have power as 0,1

3^1 * 2^0 * 7^0 (only 1 power of 3 and 0 zero power of 2 and 7 )= 3
3^1 * 2^1 * 7^0 (only 1 power of 3 and 2 zero power of 7 ) = 6
3^1 * 2^0 * 7^1 (only 1 power of 3 and 7 zero power of 2 ) =21
3^1 * 2^1 * 7^1 (all have 1 power each ) = 42
Correct Choice option is C
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Re: How many of the factors of 42 are divisible by 3 ? [#permalink] New post   27 Jun 2019, 07:36
Bunuel wrote:
How many of the factors of 42 are divisible by 3 ?

A. 2
B. 3
C. 4
D. 6
E. 8


42=2*3*7
Total# factors: 2*2*2
#Factors where the power of 3 is 1: 2*1*2= 4
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Re: How many of the factors of 42 are divisible by 3 ? [#permalink] New post   14 Sep 2019, 17:32
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julie123 wrote:
Does anyone know a shortcut to derive at "4" using the prime factorization? Or do we actually have to write down all the factors and just do the prime factorization to double-check that we have found all possible factors?



Prime factorization of 42 is 2*3*7.
total number of factors = 2*2*2 = 8

total number of factors which are not divisible by 3 is calculated by finding factors of 2*7 which is 4.
no. of factors divisible by 3 = total - no. of factors not divisible by 3
= 8-4
= 4
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Re: How many of the factors of 42 are divisible by 3 ? [#permalink] New post   19 Feb 2024, 02:53
 
soapbolt wrote:
Method i used to drive at the correct answer is following

prime Factorization of 42 = 2^1 * 3^1 * 7^1

Now any factor of 42 will be divisible by 3 when it has 3 as its prime factor , means any factor of 42, should have power of 3 as 1 and 2 and 7 can have power as 0,1

3^1 * 2^0 * 7^0 (only 1 power of 3 and 0 zero power of 2 and 7 )= 3
3^1 * 2^1 * 7^0 (only 1 power of 3 and 2 zero power of 7 ) = 6
3^1 * 2^0 * 7^1 (only 1 power of 3 and 7 zero power of 2 ) =21
3^1 * 2^1 * 7^1 (all have 1 power each ) = 42
Correct Choice option is C
 

­thank for you method­
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Re: How many of the factors of 42 are divisible by 3 ? [#permalink] New post   19 Feb 2024, 08:37
Bunuel wrote:
How many of the factors of 42 are divisible by 3 ?

A. 2
B. 3
C. 4
D. 6
E. 8

\(­42 = 2*3*7\)

For the number to be divisible by 3 we must have the factors as 3 , 6 , 21 & 42, Answer must be (C) 4
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Re: How many of the factors of 42 are divisible by 3 ? [#permalink]
19 Feb 2024, 08:37
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