Numbers & Operations
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:
  1. All whole numbers are divisible by 1.
  2. A number that ends in an even digit is divisible by 2.
  3. 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.
  4. 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.
  5. A number is divisible by 5 if it ends in 0 or 5.
  6. A number is divisible by 6 if it is even and divisible by 3. This rule is a combo of rules 2 and 3.
  7. Sadly, there is no rule for 7.
  8. 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.
  9. 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.
  10. A number is divisible by 10 if it ends in 0.
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.
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