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

Question

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

KSBGC · Answer

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.

vishalkazone · Answer

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

julie123 · Answer

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?

soapbolt · Answer

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

LeoN88 · Answer

42=2*3*7
Total# factors: 2*2*2
#Factors where the power of 3 is 1: 2*1*2= 4

ScottTargetTestPrep · Answer

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

Neferteena · Answer

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

johnnywatts · Answer

thank for you method

Abhishek009 · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards