0
The only numbers which have exactly three factors are perfect squares of prime numbers. That only gives us two results:
5^2 = 25
7^2 = 49
The squares of any other prime numbers are either too small or too large to have two digits. (The next smaller Prime number is 3, and the next larger prime number is 11.)
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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.
How many three digit even numbers are possible if the left digit cannot be zero?
450
How many three digit numbers contain no 7's?
648
How many three digit counting numbers are not multiples of 2?
There are 450 of them.
How many three digit numbers are there such whose digits sum is odd?
450.
