Prime factorising, 259875=(3×3×3)×(5×5×5)×7×11.
We know, a perfect cube has multiples of 3 as powers of prime factors.
Here, the prime factor 7 and 11 does not appear in triplet form.
Therefore, 259875 is not a perfect cube.
Since in the factorization, 7 and 11 appears only one time, we must divide the number 259875 by 7×11=77, then the quotient is a perfect cube.
∴259875÷77=3375
=15×15×15=153, which is a perfect cube.
∴ The smallest number by which 259875 should be divided to make it a perfect cube is 77.