Find the number of factors of 259 which are perfect cube.1. 72. 103.

1.	Find the number of factors of 259 which are perfect cube.1. 72. 103. 194. 6
Answer» Correct Answer - Option 1 : 7 Given: The number is 25⁹ Concept used: Factors which are perfect cube have their power as multiple of 3. Calculation: To simplify 25⁹ ⇒ 25⁹ = (5²)⁹ ⇒ 25⁹ = 5¹⁸ ⇒ 259 = (5³)⁶ According to question we have to find the number of factors which are perfect cube ⇒ Factors of 259 which are perfect cube are 5³, 5⁶, 5⁹, 5¹², 5¹⁵, 5¹⁸ and 1 ⇒ Factors of 259 which are perfect cube are 53, 253, 1253, 6253, 31253, 156253, and 1 ∴ Number of factors of 25⁹ which are perfect cube are 7.

Find the number of factors of 259 which are perfect cube.1. 72. 103. 194. 6

Answer» Correct Answer - Option 1 : 7

Given:

The number is 25⁹

Concept used:

Factors which are perfect cube have their power as multiple of 3.

Calculation:

To simplify 25⁹

⇒ 25⁹ = (5²)⁹

⇒ 25⁹ = 5¹⁸

⇒ 259 = (5³)⁶

According to question we have to find the number of factors which are perfect cube

⇒ Factors of 259 which are perfect cube are 5³, 5⁶, 5⁹, 5¹², 5¹⁵, 5¹⁸ and 1

⇒ Factors of 259 which are perfect cube are 53, 253, 1253, 6253, 31253, 156253, and 1

∴ Number of factors of 25⁹ which are perfect cube are 7.

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