find the smallest number by which 37944 must be divided to obtain a perfect cube?
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Answer:
Smallest number = 4743
Step-by-step explanation:
We factorise the given number 37944 in terms of prime numbers.
2 | 37944
2 | 18972
2 | 9486
3 | 4743
3 | 1581
17 | 527
31
∴ 37944 = 2 × 2 × 2 × 3 × 3 × 17 × 31
In order to get the smallest number by which 37944 must be divided, we find the prime factors of 37944 which are not making a cube, and they are 3, 3, 17 and 31.
∴ the required smallest number is
= 3 × 3 × 17 × 31 = 4743
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