Question

What is the least positive multiple of 25 for which the product of its digits is also a positive multiple of 25?

Answer 1

The multiples of 25 are 1,5,25
If you chose 1, the lowest quantity thats postive, there is one digit,1, so 1*1=1
1 is a multiple of 25
so your answer is 1

Answer 2

525

Explanation:

Every multiple of 25 ends in 00, 25, 50, or 75. Since we want the product of the digits to be a positive multiple of 25, the final two digits must be either 25 or 75.

A nonzero product of digits is a multiple of 25 exactly when two or more of the digits is are equal to 5. If a number ends in 75 and the product of its digits is a multiple of 25, then replacing 75 by 25 in that number will also give a smaller number whose product of digits is a multiple of 25. Therefore we are looking for a number whose final two digits are 25 and for which 5 is one of the other digits.

Since 525 is the smallest such number, the answer must be 525