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Hello i'm acually a student who needs help with math. My question is: Why is it that when you add the digits of a number you can tell what the multiples of that number are. 1+2+1+2+1+3+1+1+1=18, therefore 12131313111 is divisble by 2, 9, 18, & 3 because those numbers are divisble by 18. The rule for checking divisibility by adding the digits is something that works for 3 and 9 but not for 2. A number is divisible by 2 precisely when the last digit of the number is divisible by 2. Thus 376 and 2796520 are divible by 2 since 6 and 0 are divisible by 2, but 2975 and your number 2131313111 are not since 5 and 1 are not divisible by 2. To see why this works for 9 look at look at an example, say 2427. = 2x1000 + 4x100 + 2x10 + 7 = 2x(999+1) + 4x(99+1) + 2x(9+1) + 7 = 2x999 + 2x1 + 4x99 + 4x1 + 2x9 + 2x1 + 7 = 2x999 + 4x99 + 2x9 + (2 + 4 + 2 + 7) = 9(2x111 + 4x11 + 2x1) + (2 + 4 + 2 + 7) 2427 = 9(2x111 + 4x11 + 2x1) + (2 + 4 + 2 + 7) * On the right side, 9 divides 9(2x111 + 4x11 + 2x1) and thus if 9 divides 2 + 4 + 2 + 7, the sum of the digits, then 9 divides 2427.
The equation marked * can be rewritten In this example 9 does not divide 2 + 4 + 2 + 7 = 15 so 9 does not divide 2427. For divisibility by 3 look at the equation marked * again. On the right side, 3 divides 9(2x111 + 4x11 + 2x1) and thus if 3 divides 2 + 4 + 2 + 7, the sum of the digits, if and only is 3 divides 2427. Here 3 does divide 2 + 4 + 2 + 7 = 15 and hence 3 divides 2427. I hope this helps,Penny
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