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The three perfect numbers under 500 are 6, 28, and 496. A perfect number is defined as a positive integer that is equal to the sum of its proper divisors, excluding itself. For example, the divisors of 6 are 1, 2, and 3, which sum to 6; for 28, the divisors are 1, 2, 4, 7, and 14, summing to 28; and for 496, the divisors are 1, 2, 4, 8, 16, 31, 62, 124, and 248, which also sum to 496.
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What are the perfect squares from 1 to 500?
Perfect squares are the result of multiplying integers by themselves: 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 etc. The perfect squares, above, are the numbers to the right of the equal sign, so just continue until you pass the number 500.
How many perfect cubes are there from 1 to 500?
To find the perfect cubes from 1 to 500, we identify the integers whose cubes are less than or equal to 500. The perfect cubes in this range are (1^3 = 1), (2^3 = 8), (3^3 = 27), (4^3 = 64), (5^3 = 125), (6^3 = 216), and (7^3 = 343). The next integer, (8^3 = 512), exceeds 500. Therefore, there are a total of 7 perfect cubes from 1 to 500.
What 3 prime numbers multiplied equal 500?
You'll need five. 2 x 2 x 5 x 5 x 5 = 500
Can you write every integer as the sum of two nonzero perfect squares?
No.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theorem
What natural numbers less than 750 are both perfect squares and perfect cubes?
Natural numbers that are both perfect squares and perfect cubes are perfect sixth powers, since the least common multiple of 2 and 3 is 6. The perfect sixth powers less than 750 are (1^6 = 1), (2^6 = 64), and (3^6 = 729). Therefore, the natural numbers less than 750 that are both perfect squares and perfect cubes are 1, 64, and 729.
How many 3 digit numbers are under 500?
The 3 digit numbers under 500 are 100 through 499.
What are the perfect squares from 1 to 500?
Perfect squares are the result of multiplying integers by themselves: 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 etc. The perfect squares, above, are the numbers to the right of the equal sign, so just continue until you pass the number 500.
How many perfect cubes are there from 1 to 500?
To find the perfect cubes from 1 to 500, we identify the integers whose cubes are less than or equal to 500. The perfect cubes in this range are (1^3 = 1), (2^3 = 8), (3^3 = 27), (4^3 = 64), (5^3 = 125), (6^3 = 216), and (7^3 = 343). The next integer, (8^3 = 512), exceeds 500. Therefore, there are a total of 7 perfect cubes from 1 to 500.
What numbers are not divisible by 2 and 3 under 500?
There are 417 of them and it would take too long to list them all. You could draw up a list of all 500 numbers and then delete each multiple of 6. There are 83 of them.
How many numbers between 1 to 500 is divisible by 3 or 5?
There are 232 numbers between 1 and 500 that are divisible by 3 or 5.
Are 12 3 and 4 perfect numbers?
No.
What 3 prime numbers multiplied equal 500?
You'll need five. 2 x 2 x 5 x 5 x 5 = 500
What numbers do you divide to get 500?
1000 (2)1500 (3)
How many 3 digit numbers between 99 to 500?
400 of them.
What 3 numbers can you multiply to get 500?
1500
The natural numbers are closed under division?
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
What is the sum of the first 500 numbers?
The sum of the first 500 positive integers is: 1 + 2 + 3 + ... + 498 + 499 + 500 = 125250
