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

###### Related Articles

- Divisibility by 4 – Principles & Trick (mathchat.wordpress.com)
- Divisibility: Find out if 3 divides evenly into an integer (mathchat.wordpress.com)
- Prime and Composite Number Game (brighthub.com)
- From GPGCF to GCF … in two easy steps (mathchat.wordpress.com)

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