Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# math question?

The sum of the squares of the positive factors of a positive integer is 1300, and the sum of the positive factors of the square of the integer is 2821. Find the square of the sum of the positive factors of the integer.

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Well, 1300 is the sum of the squares of the positive factors of 30. {1365 is the sum of the squares of the positive factors of 32 (being 2⁵), so it was going to be nearby}

The factors of 30² are 900, 450, 300, 225, 180, 150, 100, 90, 75, 60, 50, 45, 36, 30, 25, 20, 18, 15, 12, 10, 9, 6, 5, 4, 3, 2, and 1 which sum to 2821, so that checks out.

The square of the sum of the positive factors of 30 is (30 + 15 + 10 + 6 + 5 + 3 + 2 + 1)² which is 72² which is 5184.

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• The sum of the squares of the positive factors of a positive integer is 1300,

and the sum of the positive factors of the square of the integer is 2821.

Factorization:

1300 = 22 × 52 × 13

The square of the sum of the positive factors of the integer:

87^2 = 7569

Factorization:

2821 = 7 × 13 × 31

The square of the sum of the positive factors of the integer:

51^2 = 2601

• Krishnamurthy
Lv 7
1 month agoReport

1300 = 2^2 × 5^2 × 13  The square of the sum of the positive factors of the integer:  27^2 = 729

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