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 Module 3-1 Divisibility Rules 2 – A number is divisible by 2 if the last digit is even (example: 49,366) 3 – A number is divisible by 3 if the sum of the digits is divisible by 3 example: 9,456,336 = 9 + 4 + 5 + 6 + 3 + 3 + 6 = 36 (yes) 4 – A number is divisible by 4 if the last 2 digits are divisible by 4 or if they are zeros example: 9,456,336 – 36 is divisible by 4 so the whole number is divisible by 4 5 – A number is divisible by 5 if the last digit is 0 or 5 example: 9,456,350 or 7,865 6 – A number is divisible by 6 if it is divisible by 2 and 3 example: 877,842 – it is even so it is divisible by 2 and 8 + 7 + 7 + 8 + 4 + 2 = 36 so it is divisible by 3 therefore it must be divisible by 6 7 – A number is divisible by 7 if you double the rightmost digit and subtract it from the remaining digits. If the result is divisible by 7 then the whole number is divisible by 7. You may keep doubling and subtracting until the result is small enough for you to tell if it is divisible. Example: 2457 – double the 7 = 14 subtract the 14 from 245 you get 231 – now double the 1 = 2 subtract the 2 from 23 you get 21 – 21 is divisible by 7 so 2457 must also be divisible by 7 ******This is not necessary to learn****** **********************BONUS****************************** 8 – A number is divisible by 8 if the last 3 digits are divisible by 8 or are all zero. example: 7,653,048 or 7,653,000 9 – A number is divisible by 9 if the sum of the digits is divisible by 9 example: 78,363 – 7 + 8 + 3 + 6 + 3 = 27 is divisible by 9 so the whole number is divisible by 9 10 – A number is divisible by 10 if the last digit is a 0. Example: 56,780