48 Part 1: The World of Numbers
There are a few shortcuts, like recognizing even numbers (numbers that end in 0, 2, 4, 6, or 8)
and multiples of 5 (numbers that end in 5 or 0). You can check if a number is divisible by 3 by
adding the digits. If the sum is divisible by 3, so is the original number. If you get a large number
as the sum of the digits and you don’t know if it’s divisible by 3, you can add the digits again. You
can add the digits as many times as necessary until you can decide if the sum is a multiple of 3.
For example, to see if 45,829 is a multiple of 3, add 4 + 5 + 8 + 2 + 9 = 28. Is 28 a multiple of 3?
It’s not, but if you’re not sure, add 2 + 8 = 10. You know 10 is not a multiple of 3, so 45,829 is not
a multiple of 3.
The same idea will work for 9. If you add the digits and get a multiple of 9, the original number is
divisible by 9. Here’s a chart of the tests you might want to remember.Tests for Divisibility
Multiple of: Test Example
2 Ends in 2, 4, 6, 8, or 0. 45,938 is a multiple of 2 because it ends in- 673 is not a multiple of 2.
3 Sum of the digits is divisible by 3. 9,348 is a multiple of 3 because
9 + 3 + 4 + 8 = 24, which is a multiple of - (Check 2 + 4 = 6, a multiple of 3.)
4 The last two digits are a multiple of 4. 35,712 is a multiple of 4 because the last
two digits, 12, is a multiple of 4.
5 Ends in 5 or 0. 74,935 and 680 are multiples of 5.
6 If it’s a multiple of 2 and a multiple of 3,
it’s a multiple of 6.
65,814 is a multiple of 2 because it ends
in 4. It’s a multiple of 3 because
6 + 5 + 8 + 1 + 4 = 24, a multiple of 3.
So 65,814 is a multiple of 6.
8 The last 3 digits are a multiple of 8. 42,864 is a multiple of 8 because 864 is
a multiple of 8.
9 Sum of the digits is a multiple of 9. 39,348 is a multiple of 9, because
3 + 9 + 3 + 4 + 8 = 27, a multiple of 9.
10 Ends in 0. 483,940 is a multiple of 10.Sometimes, to find out if a number has any factors, or divisors, other than itself and 1, you have
no choice but to just divide by each of the primes. The number 901 is not even, so 2 is not a fac-
tor. Its digits add to 10, so it’s not divisible by 3. It doesn’t end in 5 or 0, so it’s not a multiple of 5.
But you just have to divide by 7 and see what happens. 901 z 7 = 128 with 5 left over, so 7 is not
a factor. 11 is the next prime, but 901 z 11 is 81 with 10 left over, so 11 is not a factor.