Question

) 259875 should be divided by _________ to make it a perfect cube.

Answer 1

Answer:

77

Step-by-step explanation:

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Answer 2

Answer:

77

Step-by-step explanation:

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=15

3

, which is a perfect cube.

∴ The smallest number by which 259875 should be divided to make it a perfect cube is 77.

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