Divisibility and Remainders
This is division, old-school style. Actually, division,
grade-school style is probably more accurate. There are a bunch
of divisibility rules that you learned in grade school,
then quickly forgot. The SAT dusts them off and showcases them in
an item or two, so here’s a trip down memory lane:
-
All whole numbers are divisible by 1.
- A
number that ends in an even digit is divisible by 2.
- A
number is divisible by 3 if its digits add up to a number divisible by
3. For example, 384 is divisible by 3 because 3 + 8 + 4 = 15, and
15 is divisible by 3.
- A
number is divisible by 4 if its last two digits are divisible by
4. The number 5,764 is divisible by 4 because 64 is divisible by
4.
- A
number is divisible by 5 if it ends in 0 or 5.
- A
number is divisible by 6 if it is even and divisible by 3. This
rule is a combo of rules 2 and 3.
- Sadly,
there is no rule for 7.
- A
number is divisible by 8 if its last three digits are divisible
by 8. For example, 1,249,216 is divisible by 8 because 216 is divisible
by 8.
- A
number is divisible by 9 if its digits add up to a number divisible by
9. The number 2,952 is divisible by 9 because 2 + 9 + 5 + 2 = 18.
- A
number is divisible by 10 if it ends in 0.
Remainders
When all of us have calculators embedded in our forearms, remainders will finally
become extinct. Until then, remainders will continue their marginalized
existence. A remainder is the integer left over after one number has
been divided into another. In the following example, the remainder
is 3, and the dividend is 4:
Because you get to use a calculator on the exam and because
remainders show up as fractions or decimals on calculators, the
SAT includes one or two remainder items to trick you up.
