Lesson: Divisibility Rules

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Hi, are there any similar rules for 7? How do we determine if a large number is divisible by 7 and also by other prime numbers?
gmat-admin's picture

There are other rules for other numbers (like 7, 8, 11, etc), but I've never seen an official GMAT question that requires those rules. So, we have left them out.

Sure, thanks!
And thank you for this really wonderful video course!
gmat-admin's picture

Glad you like it!

Hey, how come we say that 0 is divisible by 4? I know that it has no remainder, but it doesn't make much sense to me. Say we have 8 cookies to be divided on 4 people, then each person gets 2 cookies and we have no remainder, so 8 is divisible by 4. But if we have 0 cookies and we want to divide that on 4 people, well, they'll be disapointed since they won't be getting any cookies, so we don't have anything to give, and therefore we don't have any remainder either. Any additional thoughts or any logical explanation? :-)
gmat-admin's picture

Hi Byefox,

20 is divisible by 4, because we can take 20 cookies and divide them into 4 EQUAL groups of 5 cookies each.

Likewise, 0 is divisible by 4, because we can take 0 cookies and divide them into 4 EQUAL groups of 0 cookies each.

Quote from the Official Guide for GMAT Review:

"If x and y are integers and x ≠ 0, then x is a divisor (factor) of y provided that y = xn for some integer n. In this case, y is also said to be divisible by x or to be a multiple of x.

For example, 7 is a divisor or factor of 28 since 28 = (7)(4), but 8 is not a divisor of 28 since there is no integer n such that 28 = 8n"

So, 12 is divisible by 4, since we can write 12 = (4)(3), where 3 is an integer.

Likewise, 44 is divisible by 4, since we can write 44 = (4)(11), where 11 is an integer.

AND, 0 is divisible by 4, since we can write 0 = (4)(0), where 0 is an integer.

Does that help?

Cheers,
Brent

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