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.