How to Use the Prime & Perfect Square Checker
Enter any integer from 1 to 10,000,000 and this tool instantly checks several mathematical properties simultaneously. It tells you whether the number is prime (has exactly two divisors: 1 and itself), a perfect square (equal to some integer squared), and a perfect number (the sum of all proper divisors equals the number). It also shows the even/odd status, total divisor count, sum of all divisors, and the full divisor list.
For example, entering 28 reveals that it is not prime (it has 6 divisors: 1, 2, 4, 7, 14, 28), not a perfect square, but is a perfect number because 1+2+4+7+14 = 28. Entering 36 shows it is a perfect square (6² = 36), not prime, not a perfect number. Perfect numbers are extremely rare — only 6, 28, 496, and 8,128 exist below 10,000,000.
This checker is useful for learning number theory, verifying homework, or exploring the properties of integers. The divisor list shows up to 30 values with a total count if there are more.
Frequently Asked Questions
An integer n where √n is also an integer. Examples: 1, 4, 9, 16, 25, 36 (n = 1², 2², 3², 4², 5², 6²).
A perfect number equals the sum of its proper divisors (all divisors except itself). Only four exist below 10 million: 6, 28, 496, and 8128.
No. By definition, a prime must have exactly two distinct factors. The number 1 has only one factor (itself), so it is classified as neither prime nor composite.