Question

There are 312 students in 4 fifth grade classes. Which of the following helps determine of 312 is divisible by 4?

A 12 is divisible by 4, so 312 is divisible by 4
B 312 is even, so 312 is divisible by 4
C 312 does not end in a 4 or an 8, so 312 is not divisible by 4
D 3 + 1 + 2 = 6 and 6 is not divisible by 4, so 312 is not divisible by 4

Please explain the answer

Answer 1

A. 12 is divisible by 4, so 312 is divisible by 4

Explanation:

312/4 = (300 +12)/4 = 300/4 + 12/4 = 75 + (12/4)

100 is divisible by 4, so any number of hundreds will be divisible by 4. In the problem at hand, we know 300 is divisible by 4.

After subtracting the hundreds (and multiples of 100) from the number, we get 12. The number will be divisible by 4 if 12 is divisible by 4.

_____

Another way to check for divisibility by 4 is to see if the number can be divided by 2 twice. The result of the first division by 2 is 156, and this number is even, so we know it can be divided by 2 again. Since 2·2=4, we know a number divisible twice by 2 will be divisible by 4: n/4 = n/(2·2) = (n/2)/2. (Again, we only need to be concerned with the last 2 digits, since we already know multiples of 100 are divisible by 4.)