How many positive integers will divide evenly into 520?

Question

A. 8 
B. 12 
C. 16 
D. 18 
E. 20

OptimusPrepJanielle · Answer

520 = 10*13*4 = 8*5*13 = 2^3*5*13

We need to positive integers will divide evenly into 520 or simply the factors of 520

If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)

Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 16

Option C

TarPhi · Answer

What does divide evenly really mean?

It is not, no. of even divisors, right?

Bunuel

chetan2u · Answer

Here evenly is not related to even-odd. Evenly means equally, so factors that completely divide 520 without leaving decimals. 
Example. 
9 is evenly divisible by 1,3 and 9. 
But 7 is not evenly divisible by 3 as it leads to a remainder 1.

chetan2u · Answer

For finding factors, either use the formula or calculate for each factor, a method that can be time consuming.

Formula
Get the number into its prime factor. 
520 =2*5*52=2*5*2*26=2*2*2*5*13 2^3*5*13 
Number of factors = (3+1)(1+1)(1+1)=4*2*2=16

Calculate 
520=1*520=2*260=4*130=5*104=8*65=10*52=13*40=20*26
So 1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
16

C

TarPhi · Answer

Thank  chetan2u

Just to confirm no. of factors is 16.

If they had asked 
no of odd factors, it would've been 4
no of even factors, it would've been 12

Yeah?

chetan2u · Answer

Yes,

Odd factors will consist of 5*13, so (1+1)(1+1)=4
Even factors = 16-4=12

ScottTargetTestPrep · Answer

Solution:

Since we need to determine the number of factors of 520, we need to prime factorize 520:

520 = 52 x 10 = 4 x 13 x 2 x 5 = 2^3 x 5^1 x 13^1

The number of positive factors of any integer is obtained by adding 1 to each exponent of the integer’s prime factorization and then multiplying those “adjusted” exponent numbers. Thus, we see that 520 has (3 + 1)(1 + 1)(1 + 1) = 4 x 2 x 2 = 16 factors.

Answer: C

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 positive integers will divide evenly into 520?

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 positive integers will divide evenly into 520?

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