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If a679b is a 5-digit no. in base 10 and is divisible by 72 the the values of a and b are?

If a679b is a 5-digit no. in base 10 and is divisible by 72 the the values of a and b are?

Grade:11

1 Answers

Aiman Saad Baig
39 Points
10 years ago
Base = the number which the digits of the number represent powers of. Base 10 is our normal numbering system where the rightmost digit represents 1`s, and then going left, 10`s, 10^2`s or 100`s, etc. If a number is divisible by 72 it is divisible by 9, and the sum of its digits is also divisible by 9. 6+7 = 13 = 9 + 4 so the remaining digits must sum to 5 or 14. If it is divisible by 8, it is even, so the possible digits are limited to 6...8, 8...6, 1...4, and 3...2 If a number is divisible by 8, since 1000 is divisible by 8, its last 3 digits are divisible by 8. 796, 798, and 794 are not, but 792, So, the number is 36792 which is 72 * 511.

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