Chapter 1.6 (Mathematics 5)

Divisibility tests of 2, 5 and 10

A divisibility test is a quick way to check whether a number is divisible by another number without a remainder.

Divisibility test of 2

In pairs:

  1. Divide each of the following numbers by 2: 2, 11, 24, 30, 41, 78, 95, 59, 63 and 76.
  2. List the numbers divisible by 2.
  • 2
  • 11
  • 24
  • 30
  • 41
  • 78
  • 95
  • 59
  • 63
  • 76
  1. What do you notice about digit in the ones place value in each number divisible by 2?
  2. Discuss and share the results with other groups.

Note

The last digit in a number divisible by 2 is 0, 2, 4, 6 or 8.

Example 10

Which of the following numbers are divisible by 2?

8, 13, 17, 24, 31, 50, 82 and 106.

The numbers divisible by 2 are:
​8, 24, 50, 82 and 106 because the last digit in each number is even number.

Exercise L

  • 23
  • 46
  • 148
  • 953
  • 75
  • 3 128
  • 121
  • 122
  • 123
  • 124
  • 125
  • 126
  • 127
  • 128
  • 129
  • 130
  • 131
  • 132
  • 133
  • 134
  • 135
  • 136
  • 137
  • 138
  • 139
  • 140
  • 141
  • 7
  • 16
  • 21
  • 38
  • 11
  • 28
  • 71
  • 80

L5

Use IT devices to learn more about divisibility test of 2.

Divisibility test of 5

In pairs:

  1. Divide each of the following numbers by 5: 11, 15, 19, 32, 45, 58, 60, 64 and 70.
  2. Check the last digit of each number divisible by 5.
  • 0
  • 1
  • 2
  • 4
  • 5
  • 8
  • 9
  1. Discuss and share the results with other groups.

Example 11

Without carrying out the actual division, find which of the following numbers are divisible by 5:

  1. 186
  2. 3 540
  1. 56 615
  2. 95 689
  1. The digit in the ones place value in 3 540 is 0. So 3 540 is divisible by 5.
  2. The digit in the ones place in 56 615 is 5. So 56 615 is divisible by 5.

Exercise M

  • 6815
  • 65 403
  • 41 630
  • 80 206
  • 4729
  • 24 320
  • 19 867
  • 11 315
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 0

27

53

156

721

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 0

36

59

187

2803

Divisibility test of 10

In pairs:

  1. Identify numbers that are multiples of 10 in the following list:
    15, 18, 20, 38, 40, 46, 49, 50, 61, 72 and 100.
  2. What is the last digit in each multiple of ten? 
  3. Discuss and share your findings with other groups.

Note

Multiples of 10 are all divisible by 10.

Example 12

Without carrying out the actual division, find which of the following numbers are divisible by 10?
  1. 5 260
  2. 35 165
  1. 69 150
  2. 10 108
  1. 5 260 is divisible by 10 because the digit in ones place value is 0.
  1. 69 150 is divisible by 10 because the digit in ones place value is 0.

Exercise N

  • 7 480
  • 29 536
  • 9 835
  • 35 690
  • 12 700

  • 8 935 kg
  • 15 260 kg
  • 86 126 kg
  • 11 900 kg
  • 9 865
  • 11 250
  • 23 498
  • 29 600

Divisibility test of 2 , 5 and 10

Example 13

Which of the following numbers are divisible by both 2 and 5?

45, 60, 72, 5, 160, 324, 425, 20, 1 000.

The numbers 60, 160, 920, 1 000 are divisible by both 2 and 5.

A number is divisible by both 2 and 5 if the digit in the ones place value is zero (0).

Exercise P

  • 36
  • 43
  • 44
  • 70
  • 87
  • 92
  • 125
  • 146
  • 339
  • 23
  • 35
  • 57
  • 65
  • 121
  • 140
  • 209
  • 1026
  • 1160
  • 150
  • 165
  • 3080
  • 4950
  • 6675
  • 8001
  • 9000
  • 120
  • 135
  • 182
  • 250
  • 285
  • 400
  • 525
  • 932
  • 1100
  • 80
  • 142
  • 250
  • 255
  • 310
  • 455
  • 698
  • 1080

2

  • 50
  • 65
  • 90
  • 96

5

  • 50
  • 65
  • 90
  • 96

10

  • 50
  • 65
  • 90
  • 96
  • 90
  • 105
  • 130
  • 300
  • 455
  • 950
  • 2 245
  • 3 600

Digital Time

Divisibility test of 2, 5 and 10