Source: Official Guide Revised GRE 1st Ed. Arithmetic Exercises; #3

2

# Which of the integers 312, 98, 112, and

Which of the integers 312, 98, 112, and 144 are divisible by 8?

### 1 Explanation

1

Bridget Lekota

312, 98,112 DIVISIBLE BY 8?
= 3+1+2 =6
9+8 = 17
1+1+2 =4

=6+17+4
=27

Jul 6, 2017 • Comment

Sam Kinsman, Magoosh Tutor

Hi Bridget,

Unfortunately, when we're testing for divisibility by 8, adding all the digits doesn't really help.

One thing we can do is see if we can divide each number by 2 three times. We know that 2*2*2 = 8. So if we can divide a number by 2 three times, it means the number is divisible by 8.

312 / 2 = 156
156 / 2 = 78
78 / 2 = 39

So 312 is divisible by 8.

98 / 2 = 49
49 is not divisible by 2, so 98 is not divisible by 8.

112 / 2 = 56
56 / 2 = 28
28 / 2 = 14

So 112 is divisible by 8.

144 / 2 = 62
62 / 2 = 31
31 is not divisible by 2, so 144 is not divisible by 8.

I hope this helps!

Fabiola Baltodano

Would the rule of decomposing the divisor (in this case 8) apply for any divisor? For instance, if the divisor was 6 (= 2x3) instead of 8, would only the integers divided by 2 and then by 3, or vice-versa, be divisible by 6?

Sam Kinsman, Magoosh Tutor

Yes, that's right! :)