Productively small

Probability Level 2

What is the sum of all positive integers less than 100 that have the product of their digits equal to 4?

Details and assumptions

Clarification: The empty product (product of 0 numbers) is defined to be 1. The product of a number is the number itself.

The answer is 81.

1 solution

Arron Kau Staff
May 13, 2014

Numbers less than 100 have either 1 digit or 2 digits. The number $4$ is the only $1$ -digit number with its product of digits equal to $4$ . If we have a two digit number, the digits must either both be $2$ , in which case we have the number $22$ , or the digits are $1$ and $4$ , in which case we have the numbers $14$ and $41$ . The sum of these numbers is $4 + 22 + 14 + 41 = 81$ .

Productively small

The answer is 81.

1 solution

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