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How many 5-digit integers are perfect squares?
The smallest 5-digit integer perfect square is 10,000 = (100)2The largest 5-digit integer perfect square is 99,856 = (316)2So we want to know how many numbers that is, from 100 to 316 inclusive.It's 316 minus the first 99 = 217 of them.
How many two digit numbers have digits whose sum is a perfect square?
69
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 2 digits numbers are such that the difference of the number and the number with the digits reversed is a perfect square?
If the number with the digits reversed can have a leading 0 so that it is a 1-digit number, then 16. Otherwise 13.
