Divisibility Stage 4 Year 7 Press CtrlA 2009

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=23 r 1 » 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 Positions Odd = Even so divisible by 11 3214 » 2+4=6 » Odd 3+1=4 » Even E 0 Positions Odd ≠ Even so Not divisible by 11 42 11

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