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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 Example: We can ÷ “3” 471 ÷ 3? …when the sum of all digits is a number that can be divided by 3 4 + 7 + 1 = 12 12 ÷ 3? yes, so… 471 ÷ 3 = yes Divisibility by 3, 6, 9 Can we ÷ 3?? 78 ÷ 3 7 + 8 = 15 15 ÷ 3 = yes 458 ÷ 3 4 + 5 + 8 = 17 17 ÷ 3 = no 9270 ÷ 3 9 + 2 + 7 + 0 = 18 18 ÷ 3 = yes Divisibility by 3, 6, 9 Example: We can ÷ “6” 108 ÷ 6? …when the number can be divided by 2 AND 3 last digit ÷ 2 sum of digits ÷ 3 Last digit = 8 8 ÷ 2? Yes 1+0+8=9 9 ÷ 3 = yes therefore… ÷ 6 Divisibility by 3, 6, 9 Can we ÷ 6?? 7602 ÷ 6 last digit = 2 2 ÷ 2 = yes 7 + 6 + 0 + 2 = 15 15 ÷ 3 = yes 3783 ÷ 6 last digit = 3 3 ÷ 2 = no 3 + 7 + 8 + 3 = 21 21 ÷ 3 = yes Divisibility by 3, 6, 9 Example: We can ÷ “9” 513 ÷ 9? …when the sum of all digits is a number that can be divided by 9 5+1+3=9 9 ÷ 9? yes, so… 513 ÷ 9 = yes Divisibility by 3, 6, 9 Can we ÷ 9?? 7470 ÷ 9 7 + 4 + 7 + 0 = 18 18 ÷ 9 = yes *can also be ÷ 3 2568 ÷ 9 2 + 5 + 6 + 8 = 21 21 ÷ 9 = no *BUT can be ÷ 3 Divisibility by 3, 6, 9 Can it be ÷ 3, 6, or 9?? a) 7602? b) 6246? c) 578,564?