## How many even divisors of 1600 are not multiples of 16?

##### This topic has expert replies
Legendary Member
Posts: 1272
Joined: 01 Mar 2018
Followed by:2 members

### How many even divisors of 1600 are not multiples of 16?

by Gmat_mission » Sun Jun 13, 2021 10:04 am

00:00

A

B

C

D

E

## Global Stats

How many even divisors of 1600 are not multiples of 16?

(A) 4
(B) 6
(C) 9
(D) 12
(E) 18

Source: Veritas Prep

### GMAT/MBA Expert

GMAT Instructor
Posts: 2612
Joined: 02 Jun 2008
Location: Toronto
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

### Re: How many even divisors of 1600 are not multiples of 16?

by Ian Stewart » Mon Jun 14, 2021 4:09 am
We can prime factorize:

1600 = 16*100 = (2^4)(2^2)(5^2) = 2^6 * 5^2

Any divisor of 1600 thus has to look like (2^a)(5^b), where a is between 0 and 6 inclusive, and b is between 0 and 2 inclusive. If our divisor must be even, we must have at least one '2', so a must be at least 1. If our divisor is not to be a multiple of 16, then a must be less than 4. So we have three possible values of a (1, 2 and 3), and three possible values of b (0, 1 and 2), and thus 3*3 = 9 options in total.
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

• Page 1 of 1