### How to Find out if 6 Divides in Evenly – Divisibility by 6

So far we’ve learned fun & easy divisibility tricks for the numbers 3 and by 4. Learning these tricks helps us reduce fractions with serious speed, and it helps us perform other math operations with a lot more ease. So let’s keep the learning

process going.

*[Note: If this is the first of these divisibility blogs that you have seen, search this blog for posts about divisibility by 3 and by 4; that way you’ll get caught up with the flow of these posts.] *

The trick for 5 is incredibly simple: 5 goes into any number with a ones digit of 5 or 0. That is all you need to know. Not much else to say about 5.

And here is the trick for 6: 6 divides into any number that is divisible by BOTH 2 and 3. In other words, for the number in question, check to see if both 2 and 3 go in evenly. If they do, then 6 must also go in evenly. But if EITHER 2 or 3 does NOT go into the number, then 6 definitely will NOT go in. So you need divisibility by BOTH 2 AND 3 … in order for the trick to work.

Here’s an alternative way to say this trick, a way some kids find easier to grasp: “6 goes into all even numbers that are divisible by 3.”

EXAMPLE 1: 74 — 2 goes in, but 3 does not, so 6 does NOT go in evenly.

EXAMPLE 2: 75 — 3 goes in, but 2 does not, so 6 does NOT go in evenly.

EXAMPLE 3: 78 — 2 and 3 BOTH go in evenly, so 6 DOES go in evenly.

Notice that since the tricks for 2 and 3 are quite simple, this trick for 6 is really quite simple too. It is NOT hard to use this trick even on numbers with a bunch of digits.

EXAMPLE 4: 783,612 — 2 goes in, and so does 3, so 6 DOES go in evenly. [checking for 3, note that you need to add only the digits 7 & 8. 7 + 8 = 15, a multiple of 3, so this large number IS divisible by 3.]

Now give this a try yourself with these numbers. For each number tell whether

or not 2, 3 and 6 will divide in evenly.

**PROBLEMS:**

a) 84

b) 112

c) 141

d) 266

e) 552

f) 714

g) 936

h) 994

i) 1,245

j) 54,936

**ANSWERS**:

a) 84: 2 yes; 3 yes; 6 yes

b) 112: 2 yes; 3 no; 6 no

c) 141: 2 no; 3 yes; 6 no

d) 266: 2 yes; 3 no; 6 no

e) 552: 2 yes; 3 yes; 6 yes

f) 714: 2 yes; 3 yes; 6 yes

g) 936: 2 yes; 3 yes; 6 yes

h) 994: 2 yes; 3 no; 6 no

i) 1,245: 2 no; 3 yes; 6 no

j) 54,936: 2 yes; 3 yes; 6 yes

**Josh Rappaport is the author of five books on math, including the Parents Choice-award winning Algebra Survival Guide. If you like how Josh explains these problems, you’ll certainly like the Algebra Survival Guide and companion Workbook, both of which are available on Amazon.com Just click the links in the sidebar for more information! **

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