1. 7’s Chris Clements Properties of Number Divisibility tests 8’s9’s

2. Learning Objective:

3. 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.

4. 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.

5. First look at the last 3 digits; 1272 *8 does not go exactly into 100 but does go into a 1000 It’s even (so it is definitely a multiple of 2) If we half it; It’s still even so 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 even so it must be a multiple of 8

6. 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;

7. 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

8. 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…

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 = 6 2) 34 – 6 =28 28 is a multiple of 7 so 343 is too Answer must be a multiple of 7

10. Divisibility Tests First double the last digit Subtract the rest of the number Answer must be a multiple of 7

11. 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 7 First double the last digit. Subtract the rest of the number. Answer must be a multiple of 7

12. Activity

13. 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 another Three-digit number that as factors of 2 and 7.