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Find the number of factors of 259 which are perfect cube.
1. 7
2. 10
3. 19
4. 6

1 Answer

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Best 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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