3 Its digits add up to a multiple of 3. 186. 1 + 8 + 6 = 15 15
= (3 × 5)4 Its last two digits form (not “add up
to”) a number divisible by 4.103,424 24 is divisible
by 4 (24 ÷ 4 = 6)5 It ends in 5 or 0. 5,746,893,7656 It is divisible by 2 and 3. 5227 There’s a rule, but it’s more
complicated than it’s worth.8 Its last three digits form a multiple of
8.10,496,832 (832 ÷ 8 =
104)
9 Its digits add up to a multiple of 9. 34,164. 3 + 4 + 1 + 6 +
4 = 18 = (2 × 9)10 It ends in 0. 1,600Using these rules, you can see—at a glance—that 32,571 is not prime. It’s
divisible by nine!
Here’s an example of the type of problem you might see on the No Calculator
section.
What is the least positive integer divisible by the numbers 2, 3, 4, and
5?
A) 30
B) 40
C) 60
D) 120Rather than do a bunch of math, just look at the answer choices. You can
immediately tell that they’re all divisible by 2 and 5 because they end in 0. You
can use the 3 rule to cross out B and the 4 rule to cross out A. That leaves C and
D, and because we want the smallest number, C is the answer.
Pay attention to italics. In this case, two of the answer choices are divisible by 2, 3, 4, and 5—but the italicized word told you which tochoose.
—Samantha