Question

What is the smallest number by which 165375 must be divided so that the quotient is a perfect cube.

Answer 1

Answer:

131 must be divided to make a perfect cube.

Step-by-step explanation:

Any number is called a perfect cube when the prime numbers multiplying to make that number have 3 numbers each. For eg - 216 is a perfect cube because it's prime factorization contains 3 six, i.e., 216 = 6 × 6 × 6 (Notice that there are three numbers of 6).

So, when 165375 goes through the process of Prime Factorization, then it's numbers are as follows 165375 = 5 × 5 × 5 × 131, there is only no. 5 which has a group of 3. So when the number is divided by 131, i.e., 5 × 5 × 5 × 131/131, then both 131 no.s are cut down. And thus, a group of 3 of 5 remains and forms a perfect cube.