Chris Clements

Properties of Number

Divisibility tests

6’s3’s

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Learning Objective:

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Divisibility tests help usidentify if a whole number

is in a specified times table

Divisibility Tests

In this lesson you will learn divisibility tests for

multiples of 3 and 6.

Today you will find out how you can test if large whole numbers are multiples of

3 and 6.

Lets start by looking at the first ten multiples of 3.

Divisibility Tests for multiples of 3

The numbers go; odd, even, odd, even but that’s not going to help

us today.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30

3, 6, 9, 1+2=3, 1+5=6, 1+8=9, 2+1=3, 2+4=6, 2+7=9, 3+0=3

Can you see what happens to the sum of the 2 digit numbers.

This pattern continues;

So the test must be; that the sum of the digits must equal a multiple

of 3 (usually 3, 6 or 9).

The pattern goes 3, 6, 9 (all multiples of 3)

Let’s test this with a large whole number, e.g. 23,301

2+3+3+0+1 = 9

3+3=6, 3+6=9, 3+9=1+2=3, 4+2=6, 4+5=9

Check on a calculator! 23,301 ÷ 3 =

7,767

Divisibility test for finding large multiples of 3 is;•add up the sum of the digits•it must equal a multiple of 3

Give it a go;

Now we will look at multiples of 6

Divisibility Tests

Lets have a look at the first ten multiples of 6.

6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Notice anything?

Just like the test for the 3’s but in a different order; 6, 3, 9…

All even numbers!

6, 1+2=3, 1+8=9, 2+4=6, 3+0=3, 3+6=9, 4+2=6, 4+8=1+2, 5+4=9,

6+0=6

Divisibility TestsSo the test for multiples of 6 is;

• is the whole number even• is the sum of digits a multiple of 3Give it a go, find the multiples of 6!

Divisibility tests for multiples of 3 and 6

1) For multiples of 3; add up the digits to see if it is a multiple of 3 (usually 3, 6 or 9)

2) For multiples of 6; first see if it is even, then see if the sum of it’s digits is also a multiple of 3 (usually 3, 6 or 9)

Divisibility tests

Steps to success

Activity

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Plenary

Look at the two number sequences; can you say a number greater than 200 which will be in both

sequences?

Use the 6 digit cards to make three multiples of 3.

More ways possible!

Many answers but the lowest possible would be 210 because it is a multiple

of 5 (ends in a 0) and it’s digits equal 3.Accept any number that satisfies this

criteria.