Question

if a679b is a five digit number in base 10 and is divisible by 72, then the values of a and b is what?

Answer 1

solution:

$Given:</p><p> If a679b is a five-digit number in base 10 and is divisible by 72</p><p>To find: the values of a and b </p> <p>Base = the number which the digits of the number represent powers of.</p> <p>Base 10 is our normal numbering system where </p><p>the rightmost digit represents 1's, and then going left, 10's, 100's, etc.</p> <p>If a number is divisible by 72 it is divisible by 9,</p><p>and the sum of its digits is also divisible by 9.</p> <p>6+7 = 13 = 9 + 4$$so the remaining digits must sum to 5 or 14.</p> <p>If it is divisible by 8, it is even, so the possible digits are limited to</p><p>6...8, 8...6, 1...4, and 3...2</p> <p>=> 3,2 is the only option we get.</p><p> </p><p>If a number is divisible by 8, since 1000 is divisible by 8,</p><p>its last 3 digits are divisible by 8.</p><p>796, 798, and 794 are not, but 792 is, so the answer is 3,2 .</p><p>and the number is</p><p> 72\times511= 36792$