# 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.

### 2 Answers

- Φ² = Φ+1Lv 73 months agoFavorite Answer
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.

- Login to reply the answers

- KrishnamurthyLv 73 months ago
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

- KrishnamurthyLv 73 months agoReport
1300 = 2^2 × 5^2 × 13 The square of the sum of the positive factors of the integer: 27^2 = 729

- Login to reply the answers