# Maths question

I can’t solve my 10 year old nieces maths question. A little help.

Multiply a three digit number that does not end in zero by a two digit number between 12-18. Your answer has to be in the 50 times table.

To be in the 50 times table (i.e. to be a multiple of 50), the result must have prime factors 5, 5, and 2. (5 x 5 x 2 = 50). That means you can choose any two numbers (satisfying the constraints given) that guarantee that the result has these prime factors.

The three-digit number cannot end with zero (i.e. it cannot be a multiple of 10). Thus, you can’t choose a three-digit number that has both 2 and 5 as prime factors (2 x 5 = 10). The prime factor 2 must come from the two-digit number, which means that you can only choose an even two-digit number: 12, 14, 16, 18.

Thus the three-digit number must contain prime factors 5 and 5, but not 2 (i.e. it must be an odd multiple of 25). So the possibilities are as follows: 125, 175, 225, 275, … , 975.

Test it with any pair:

475 x 14 = 6650, which is divisible by 50.
725 x 18 = 13050, which is divisible by 50.