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Grade: 11

                        

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

6 years ago

Answers : (1)

Aiman Saad Baig
39 Points
							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.
						
6 years ago
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