Question

If N = 9⁸ + 9⁹ + 9¹⁰ + 9¹¹, then how many positive factors of N are there?

Options

• 102

• 108

• 204

• 128

Answer 1

204

Explanation:

N = 9⁸ + 9⁹ + 9¹⁰ + 9¹¹

N = 9⁸ (1 + 9 + 9² + 9³)

N = 9⁸ × 820

N = 3¹⁶ × 2² × 5¹ × 41¹

∴ Divisor = (16 + 1) (2 + 1) (1 + 1) (1 + 1) = 204