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### How many 3 digit numbers have even no of factors?

878 three digit numbers have an even number of factors.

Every factor of a number has a pair, so there ought to be an

even number of factors for every number. However, if a pair of the

factors are the same number, then there will be an odd number of

factors, that is if the number is a perfect square.

Assuming three digit numbers are 100 to 999:

From 100 to 999, the perfect squares are 102 = 100 to 312 = 961,

a total of 31-10+1 = 22 numbers.

So of the 999-100+1 = 900 three digit numbers, 22 have an odd

number of factors, so 900-22 = 878 have an even number of

factors.