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.