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Divisibility by 3, 6, 9

Divisibility by 3, 6, 9. Review of Divisibility. A number can be divided by… ÷ 2 when… … ending digit is EVEN (2, 4, 6, 8, 0) ÷ 5 when… … ending digit is 5 OR 0 ÷ 10 when… … ending digit is 0. Divisibility by 3, 6, 9. We can ÷ “3”

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Divisibility by 3, 6, 9

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  1. Divisibility by3, 6, 9

  2. Review of Divisibility A number can be divided by… ÷ 2 when… … ending digit is EVEN (2, 4, 6, 8, 0) ÷ 5 when… … ending digit is 5 OR 0 ÷ 10 when… … ending digit is 0

  3. Divisibility by 3, 6, 9 We can ÷ “3” …when the sum of all digits is a number that can be divided by 3 Example: 471 ÷ 3? 4 + 7 + 1 = 12 12 ÷ 3? yes, so… 471 ÷ 3 = yes

  4. Divisibility by 3, 6, 9 Can we ÷ 3?? 78÷ 3 458 ÷ 3 9270 ÷ 3 7 + 8 = 15  15 ÷ 3 = yes 4 + 5 + 8 = 17  17 ÷ 3 = no 9 + 2 + 7 + 0 = 18  18 ÷ 3 = yes

  5. Divisibility by 3, 6, 9 We can ÷ “6” …when the number can be divided by 2 AND 3 • last digit ÷ 2 • sum of digits ÷ 3 Example: 108 ÷ 6? Last digit = 8 8 ÷ 2? Yes 1 + 0 + 8 = 9 • 9÷ 3 = yes therefore… ÷ 6

  6. Divisibility by 3, 6, 9 Can we ÷ 6?? 7602 ÷ 6 3783 ÷ 6 last digit = 2  2 ÷ 2 = yes 7 + 6 + 0 + 2 = 15  15 ÷ 3 = yes last digit = 3  3 ÷ 2 = no 3 + 7 + 8 + 3 = 21  21 ÷ 3 = yes

  7. Divisibility by 3, 6, 9 We can ÷ “9” …when the sum of all digits is a number that can be divided by 9 Example: 513 ÷ 9? 5 + 1 + 3 = 9 9 ÷ 9? yes, so… 513 ÷ 9 = yes

  8. Divisibility by 3, 6, 9 Can we ÷ 9?? 7470 ÷ 9 2568 ÷ 9 7 + 4 + 7 + 0 = 18 • 18 ÷ 9 = yes *can also be ÷ 3 2 + 5 + 6 + 8 = 21 • 21 ÷ 9 = no *BUT can be ÷ 3

  9. Divisibility by 3, 6, 9 Can it be ÷ 3, 6, or 9?? • 7602? • 6246? • 578,564?

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