multiple of product of its digits = multiple of sum of its digits
Source: 2000 Austria Beginners' Competition p3
October 4, 2022
number theoryproduct of digitssum of digitsDigits
Problem Statement
A two-digit number is nice if it is both a multiple of the product of its digits and a multiple of the sum of its digits. How many numbers satisfy this property? What is the ratio of the number to the sum of digits for each of the nice numbers?