SOLUTION: A three-digit number is 13 times the product of its digits. The hundreds digit is larger than either of the other two digits. What is this number?

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Question 1136134: A three-digit number is 13 times the product of its digits. The hundreds digit is
larger than either of the other two digits. What is this number?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Since the three-digit number is equal to 13 times the product of its digits, it is divisible by its hundreds digit, which is the largest of the three.
If we increase both the tens digit and the units digit to the hundreds digit, the quotient will be 111. If instead we decrease both of them to 0, the quotient will be 100.
The actual quotient is between 100 and 111, and since it is divisible by 13, it must be 104.

The product of the tens digit and the units digit is 104%2F+13=8.
Since+8=2+%2A+4=1%2A+8, the three-digit number is one of 624, 642, 918 and 981.
The only+one divisible by 13 is 13%2A6%2A+2%2A4=+624.
answer:The number is 624