is 1188 a perfect cube? if not by which smallest natural number should 1188 be divided so that the quotient is a perfect cube
Answers
Answer:
Hence, the smallest number by which 1188 must be divided to obtain a perfect cube is 2² ×11=44.
Step-by-step explanation:
We know, a perfect cube has multiples of 3 as powers of prime factors.
Here, number of 2's is 2, number of 3's is 3 and number of 11's is 1.
So we need to divide 2² and 11 from the factorization to make 1188 a perfect cube.
Hence, the smallest number by which 1188 must be divided to obtain a perfect cube is 2² ×11
Answer:
Prime factorising 1188, we get,
1188=2×2×3×3×3×11
=2^2x 3^3 x 11
We know, a perfect cube has multiples of 3 as powers of prime factors.
Here, number of 2's is 2, number of 3's is 3 and number of 11's is 1.
So we need to divide 2 ^2
and 11 from the factorization to make 1188 a perfect cube.
Hence, the smallest number by which 1188 must be divided to obtain a perfect cube is 2^2 ×11 =44.
Hence the answer is 44