A Number divide by 7
Take off the last digit and multiply it by 2
Subtract it from the digits you have left.
If the answer divides by 7 (or is zero), then your original number will also divide by 7
Try 161623?
Take off the last digit and x 2, so we get 3 x 2 = 6
Subtract this from the other digits so we get 16162 - 6 = 16156. But does this divide by 7?
Do it again! We get 1615 - (6 x 2) = 1615 - 12 = 1603. Does this divide by 7?
On we go... 160 - 6 = 154
...and on... 15 - 8 = 7 YES! 7 divides by 7, so 161623 also divides by 7
Take off the last two digits then multiply the other digits by 2.
Add your answer to the two digits you took off.
If the answer divides by 7 then your original number will also divide by 7
Try 2723
Take off the last two digits to leave 27 and then 27 x 2 = 54
Add your answer to the two digits you took off: 54 + 23 = 77.
As 77 does divide by 7 then so does 2723.
When you do any "7" tests, it's handy to remember that 77, 84, 91 and 98 all divide by 7.
A Number divide by 13
This is similar to seeing if a number will divide by 7.
Take off the last digit and multiply it by 9
Subtract it from the digits you have left.
If the answer divides by 13 (or is zero), then your original number will also divide by 13
Try 224082
Take off the last digit and x 9, so we get 2 x 9 = 18
Subtract this from the other digits so we get 22408 - 18 = 22390. But does this divide by 13?
A BIT OF EXCITEMENT! As the last digit is "0" we can just knock it off and continue testing. So does 2239 divide by 13?
We get 223 - (9 x 9) = 223 - 81 = 142. Does this divide by 13?
On we go... 14 - 18 = -4. -4 does not divide exactly by 13, so neither does 224082.
Try 224081
22408 -9 =22399 then 2239 -81= 2158 then 215 -72= 143 and finally 14 -27= -13
-13 does divide exactly by 13, therefore 224081 divides by 13 too!
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