How many factors of 240 are also multiples of 3 ?

Question

A. 5
B. 8
C. 9
D. 10
E. 20

Bunuel · Accepted Answer

Find the number of all the factors of 240 and subtract the factors which are multiples of 3 to get the number of factors which are not multiples of 3.

Factorize 240:  240=2^4*3*5 . It has (4 + 1)(1 + 1)(1 + 1) = 20 factors.

Get rid of 3, we get  80 =2^4*5 . It has (4 + 1)(1 + 1) = 10 factors.

Now, all these factors of 80 are factors 240 but are NOT multiples of 3. So, the number of factors of 240 which are also multiples of 3 is 20 - 10 = 10.

Answer: D.

PareshGmat · Answer

Answer = D = 10

240 = 2^4 * 3^1 * 5^1

Factors which are multiples of 3 are as follows

1. 3

2. 3 * 2

3.  3 * 2^2

4.  3 * 2^3

5.  3 * 2^4

6. 3 * 5

7. 3 * 5 * 2

8.  3 * 5 * 2^2

9.  3 * 5 * 2^3

10. 3 * 5 * 2^4

desaichinmay22 · Answer

take factors of 240
240= 2^4*3^1*5^1
Total factors of 240= (4+1)*(1+1)*(1+1)
=5*2*2
=20

out of total factors of 20, half will have 0 as power of 3 and half will have 1 as power of 3. It is because we have considered only 0 and 1 as power of 3 to compute total factors of 240.
Therefore factors that are multiple of 3= 20/2= 10

Ans - D

chuckkkkk · Answer

-----------
Hi Bunuel, thanks for you post! 
But could you please elaborate these steps:
 Factorize 240:  240=2^4*3*5 . It has (4 + 1)(1 + 1)(1 + 1) = 20 factors.

Get rid of 3, we get  80 =2^4*5 . It has (4 + 1)(1 + 1) = 10 factors.

Thank you.

Bunuel · Answer

Finding the Number of Factors of an Integer : First make prime factorization of an integer n=a^p*b^q*c^r , where a , b , and c are prime factors of n and p , q , and r are their powers. The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1) . NOTE: this will include 1 and n itself. Example: Finding the number of all factors of 450: 450=2^1*3^2*5^2 Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18 factors. Check for more here: math-number-theory-88376.html

CounterSniper · Answer

240 = 2^4 *3 * 5
 total factors = 5*2*2 =20
 for a factor to be multiple of 3 , it should have 3 in the no of prime factors
 total factors which are not multiple of 3 = 5*2 =10 (factors of 2^4*5 =80)
 therefore factors of 3 = total - factors which are not multiple of 3 = 20 -10 =10

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 factors of 240 are also multiples of 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 factors of 240 are also multiples of 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