By what least number should the following numbers be divided so that they become perfect cubes? Also find the numbers whose cubes the new numbers are. (1) 41472
by factorising
by factorising
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Answer:
Solution
verified
Verified by Toppr
Prime factorising, 53240=5×2
3
×11
3
.
We know, a perfect cube has multiples of 3 as powers of prime factors.
The prime factor 5 does not appear in triplet form.
Therefore, 53240 is not a perfect cube.
Since in the factorization, 5 appears only one time, we must divide the number 53240 by 5, then the quotient is a perfect cube.
∴53240÷5=10648
=22×22×22=22
3
, which is a perfect cube.
∴ The smallest number by which 53240 should be divided to make it a perfect cube is 5.