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### 11 Cards in this Set

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 When is a # divisible by 3 ? The sum of the digits is divisible by 3. Ex. 342 is divisible by 3 because 3 + 4 + 2 = 9, and 9 is divisible by 3. When is a # divisible by 4 ? The last two digits are divisible by 4 or they are 00. Ex. 724 is divisible by 4 because 24 is divisible by 4. When is a # divisible by 6 ? The # is an even #, and the sum of the digits is divisible by 3. Ex. 108 is divisible by 6 because the 108 is an even #, and 1+0+8 = 9, and 9 is divisible by 3. When is a # divisible by 7 ? The product of the units digit X 5 + all other digits is divisible by 7. Ex. 203 is divisible by 7 because 3 x 5 =15, 15 + 20 = 35, and 35 is divisible by 7. When is a # divisible by 8 ? The last three digits are divisible by 8 or they are 000. Ex. 2104 is divisible by 8 because 104 is divisible by 8. When is a # divisible by 9 ? The sum of the digits adds to 9 or is divisible by 9. Ex. 16,713 is divisible by 9 because 1+6+7+1+3= 18, and 18 is divisible by 9. When is a # divisible by 11? The difference between the sum of the evenly placed digits and the oddly placed digits is a multiple of 11 or it equals 0. Ex1. 16,940 is divisible by 11 because: ODDS 1+9+0=10; EVENS 6+4=10. Difference 10-10 =0 Ex 2. 429 is divisible by 11 because ODDS 4+9=13; EVENS =2. Difference 13-2 = 11 When is a # divisible by 12 ? The digit sum is divisible by 3 and the last two digits are divisible by 4. Ex. 624 is divisible by 12 because 6+2+4 = 12, and 12 is divisible by 3; and, 24 is divisible by 12. When is a # divisible by 13 ? The product of the units digit X 4 + all other digits is divisible by 13. Ex. 1,105 is divisible by 13 because 5x4=20, 20+110=130, and 130 is divisible by 13. When is a # divisible by 17 ? The product of the units digit X 12 + all other digits is divisible by 17. Ex. 221 is divisible by 17 because 1x12=12, 12+22=34, and 34 is divisible by 17. What is the speed method of multiplying a two digit number by 11 ? Add together the two digits and insert the result between the digits. Carry any 10 digits if necessary. Ex1. 11x26=286 computed by 2+6=8. Insert 8 between 2 & 6. Ex2. 11x87=957 computed by 8+7=15. Insert 5 between 8 & 7. Carry 1 and add to 8.