Fun & Easy Rules for Factoring with 3, 9, 4, and 8

I just found out about some neat rules for factoring that I never knew about. I wish I’d been taught these when I was in school! I don’t know why I wasn’t, because I found some other people knew them, even here in the Middle East!

I did know which numbers are divisible by two, and which are divisible by five. But I just learned how to tell which are divisible by three, nine, four, eight, and eleven! (So far, I haven’t seen any rule for seven.)

Three: A number is divisible by three if the sum of its digits is divisible by three.

1,975,287 (divisible by three)

Because: 1+9+7+5+2+8+7 = 39 (divisible by three)

Nine: A number is divisible by nine if the sum of its digits is divisible by nine.

5,649,246 (divisible by nine)

Because: 5+6+4+9+2+4+6 = 36 (divisible by nine)

Four: A number is divisible by four if the last two digits are divisible by four.

227,648 (divisible by four), because 48 is divisible by four.

Eight: A number is divisible by eight if the last three digits are divisible by eight.

398,904 (divisible by eight), because 904 is divisible by eight.

I won’t give the rule for eleven yet, because I have found some exceptions to the rule, meaning I must be doing something wrong!

Eileen

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