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Divisibility
Stage 4
Year 7
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1
Divisibility Test for “2”
A number is divisible by 2 if it is:
Examples:
Even
478
44
442
1446
224
124
32
348
If the units digit is even.
42
2
Divisibility Test for “2”
A number is divisible by 2 if it is:
Not Divisible by 2
Examples:
471
43
441
1449
223
125
37
343
If the units digit is even.
42
3
Divisibility Test for “3”
A number is divisible by 3 if:
the sum of the digits are divisible by
3.
Examples: 591 = 5 + 9 + 1 = 15
= 1 + 5 =6
Since 6 is divisible by 3, then so is 591.
634 = 6 + 3 + 4 = 13
= 1 + 3 =4
Since 4 is not divisible by 3, neither is 634.
42
4
Divisibility Test for “4”
A number is divisible by 4 if:
the number formed by the last two
digits is divisible by 4.
Examples: 312 » 12 ÷ 4 = 3
Since 12 is divisible by 3, then so is 312.
725 » 25 ÷ 4 = 6 r 1
Since 25 is not divisible by 3, neither is 312.
42
5
Divisibility Test for “5”
A number is divisible by 5 if:
the last digit is 5 or 0.
Examples:
510 »
Last Digit 0 Divisible by 5
315 »
Last Digit 5 Divisible by 5
823 »
Last Digit 3 Not Divisible by 5
42
6
Divisibility Test for “6”
A number is divisible by 6 if:
the number is divisible by 2 and 3.
Examples:
336 » Last digit even » Divisible by 2.
3+3+6=12 » 1+2=3 »
Divisible by 3.
Since 336 is divisible by 3 & 2, it is divisible by 6.
712 » Last digit even » Divisible by 2.
7+1+2=10 » 1+0=1 » Not divisible by 3.
Since 336 is not divisible by 3, it is not divisible by 6.
42
7
Divisibility Test for “8”
A number is divisible by 8 if:
the number formed by the last
three digits is divisible by 8.
Examples:
5032 » 032÷8=4 » Divisible by 8.
Since 32 is divisible by 8, so is 5032 divisible by 8.
7105 » 105÷8=23r1 » Not divisible by 8.
Since 105 is not divisible by 8, so neither is 7105.
42
8
Divisibility Test for “9”
A number is divisible by 9 if:
the sum of the digits is divisible by 9.
Examples:
7812 » 7+8+1+2=18 » 1+8=9
Divisible by 9.
12613 » 1+2+6+1+3=13 » 1+3=4
Not divisible by 9.
42
9
Divisibility Test for “10”
A number is divisible by 10 if:
the last digit is 0.
Examples:
510 »
Last Digit 0 Divisible by 10
320 »
Last Digit 0 Divisible by 10
823 »
Last Digit 3 Not Divisible by 10
42
10
Divisibility Test for “11”
A number is divisible by 11 if:
the sum of the digits in odd positions
equals the sum of the digits in the even positions,
or
they differ by a number that is divisible by 11.
Examples:
4125 » 1+5=6 » Odd 4+2=6 » Even
E 0 E 0
Positions
Odd = Even so divisible by 11
3214 » 2+4=6 » Odd 3+1=4 » Even
E 0 E 0
Positions
Odd ≠ Even so Not divisible by 11
42
11
42
12