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Q: What number is a perfect square a even number and less than 16?

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There are three perfect squares between 0 and 50 that are even.

3 is prime, 1 less than the perfect square of 4 (2x2)

256 is the greatest even square number that is less than 300.

8, 10 24, 26

One way is to get the prime factorization of the number. If every prime occurs an even number of times, it is a square, otherwise, not. Another is to estimate the square root of the number, and square it. If you get more than the number, try a lower estimate; if less, a higher one. Using interval bisection you very quickly zero in on the square root, if it is a whole number. If so, the number is a perfect square. Otherwise, you find 2 consecutive whole numbers between which is the square root, in which case it is not a perfect square.

A square number, or perfect square, is the square of an integer. 232 is less than 572, 242 is more, so it is not the square of an integer.

There is only one even prime number and that is 2 as all over even numbers can be divided by 2 and 2 is not square so there isn't a number less than 100 that is an even prime square number.

It is 64 which is also a square number

4

Every non-negative real number is a square (every number if in the complex field) so every real number greater than or equal to -1 is one less than a square. Even if you restrict yourself to perfect squares, of the form n2, then n2 - 1 = (n-1)*(n+1) is one less than a square. There are infinitely many such numbers.

Any number squared except 0 is a perfect square so it follows that prime numbers are less common than perfect squares.

5040 is not a perfect square. The greatest perfect square less than 5040 is 4900.

A beprisque number nnn is an integer which is either one more than a prime number and one less than a perfect square, or one more than a square and one less than a prime. The 5th such number is 10.

25 is a perfect square25 is the largest whole number that is less than 26

No. The only perfect numbers less than 100 are 6 and 28. All known perfect numbers are even - it is unknown whether there are odd perfect numbers.

324

It is 25.

Actually it can, if it's not the square of a prime number. For example, 144 is the square of 12; but you can also factor it as 6 x 24.

Perfect squares have odd numbers of factors. The perfect squares less than 100 are: 1,4,9,16,25,36,49,64,81,100. 64 seems to fit both criteria.

There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).

6 and 28 are perfect numbers less than 50.

It is: 25

To be a perfect square, all the primes in a number's prime factorisation must have an even power To be a perfect cube, all the primes in a number's prime factorisation must a power that is a multiple of 3 → To be a perfect square, all the primes in a number's prime factorisation must a power that is a multiple of 3 and a multiple of 2, ie the power must be a multiple of 6 The smallest prime is 2 2⁶ = 64 = (2³)² = 8² = (2²)³ = 4³ 2¹² = 4096 (too large) 3⁶ = 729 (too large) There is also 1 = 1² = 1³ Thus the whole numbers less than 100 which are both perfect squares and perfect cubes are 1 and 64.

Prime numbers, except 2, are always odd (they would not be prime if they were even cos they would be divisible by 2.) 1 less than any odd number must be an even number.

√1476 ≈ 38.419, so the largest perfect square less than 1476 would have to be 382, or 1444.