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The number of distinct prime divisors of...

The number of distinct prime divisors of the number ` 512^(3) - 253^(3) - 259^(3)` is

A

4

B

5

C

6

D

7

Text Solution

Verified by Experts

The correct Answer is:
C
`(512)^(3)-253^(3)-259^(3)`
`=(512)^(3)-[(253^(3)+(259)^(3)]`
=`(512)^(3)-(253+259)(253^(2)+259^(2)-(253)(259))`
`=(512)^(3)-(512)[253+259)^(2)-2(253)(259)-(253)(259)]`
`= 512[(512)^(2)-{(512)^(2)-3(253)(259)}]`
`=(512)[3(253)(259)]`
`=2^(9).3. (253)(259)`
`=2^(9).3(11)(23)(7)(37)`
6 prime divisors.
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