Divisibility and Remainders
The SAT sometimes tests whether you can determine if one
number is divisible by another. To check divisibility, you could
take the immense amount of time necessary to do the division by
hand and see if the result is a whole number. Or you can give yourself
a shortcut and memorize this list of divisibility rules:
Divisibility Rules
-
All whole numbers are divisible by 1.
- All
numbers with a ones digit of 0, 2, 4, 6, or 8 are
divisible by 2.
- A
number is divisible by 3 if its digits add up to a
number divisible by 3. For example, 6,711 is
divisible by 3 because 6 + 7 + 1 + 1 = 15,
and 15 is divisible by 3.
- A
number is divisible by 4 if its last two digits are
divisible by 4. For example, 80,744 is
divisible by 4, but 7,850 is not.
- A
number is divisible by 5 if it ends in 0 or 5.
- A
number is divisible by 6 if it is even and also divisible
by 3.
- There
are no rules for 7. It is a rebel.
- A
number is divisible by 8 if its last three digits are
divisible by 8. For example, 905,256 is
divisible by 8 because 256 is divisible
by 8, and 74,513 is not divisible by 8 because 513 is
not divisible by 8.
- A
number is divisible by 9 if its digits add up to a
number divisible by 9. For example, 1,458 is
divisible by 9 because 1 + 4 + 5 + 8 = 18 and 18 is divisible
by 9.
-
A number is divisible by 10 if it ends in 0.
