7’s

Chris Clements

Properties of Number

Divisibility tests

8’s9’s

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Learning Objective:

<Steps to success>

Do you remember the divisibility test for multiples of 4?

Divisibility Tests

In this lesson you will learn divisibility tests for multiples of 7, 8 and 9.

Divisibility test for multiples of 4 Look at the last 2 digits; are they

even; if so when you half them are they still even.

Divisibility Tests for multiples of 8

The test for multiples of 8 is similar.

Do you know what changes must be made?

Divisibility test for multiples of 4 Look at the last 2 digits; are they

even; if so when you half them are they still even.

First look at the last 3 digits; 1272

*8 does not go exactly into 100 but does go into a 1000It’s even (so it is definitely a

multiple of 2)

If we half it;

It’s still evenso it must be a multiple of 4

If we wanted to test if 1272 is a multiple of 8

If we half it again;

It’s still evenso it

must be a

multiple of 8

Divisibility test for multiples of 8 Look at the last 3 digits; are they

even; if you half it, is it still even; if so, half it again, the answer must be

even.

Divisibility Tests

Give it a go;

Lets have a look at the first ten multiples of 9.

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

What do you notice?

The digits add up to 9!

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

Divisibility Tests for multiples of 9

Lets find multiples of 9 by doing the divisibility test; sum of the digits = 9.

This pattern continues; 9+9=9, 1+0+8=9, 1+1+7=9, 1+2+6=9,

1+3+5=9, 1+4+4=9…

This is the test for multiples of 7

Divisibility Tests

First double the last digit

Subtract the rest of the number

Is 343 divisible by 7;1) 343 double the last digit = 62) 34 – 6 =2828 is a multiple of 7 so 343 is too

Answer must be a multiple of 7

Divisibility TestsFirst double the last digit

Subtract the rest of the number

Answer must be a multiple of 7

Divisibility tests

Steps to success

Divisibility test for multiples of 8 Look at the last 3 digits; are they

even; if you half it, is it still even; if so, half it again, the answer must be

even.Divisibility test for multiples of 9

Sum of the digits add up to 9.

Divisibility test for multiples of 7First double the last digit. Subtract the rest of the number. Answer must be a multiple of 7

Activity

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Plenary

If this number sequence is extended will the number 2140 be in it. Give reasons.

This three digit number as factors of 2 and 7

Write anotherThree-digit

number that as factors of 2 and

7.