496
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There is only one Perfect Number within this range : 496. If 2ⁿ - 1 is prime then 2ⁿ⁻¹(2ⁿ - 1) is a perfect number. In this instance n = 5 then, 2⁴(2⁵ - 1) = 16 x 31 = 496...........and 31 is a prime number.
300
To find a cube number between 400 and 600, we need to calculate the cube root of the two limits. The cube root of 400 is approximately 7.37, and the cube root of 600 is approximately 8.66. Therefore, the cube numbers between 400 and 600 are the cubes of integers between 8 and 7, inclusive. The cube of 8 is 512, which falls within the range specified.
440
400 can be factored as 24 * 52, or 22 * 22 * 52. A perfect square factor of 400 will always have an even exponent, so here is a list: 12, 22, 42, 52, 102, and 202.