find find the smallest number by which the following number must be divided to get a perfect cube
1625
10584
88209
Answers
88209. = 121
To find the smallest number by which 88209 must be divided so that the quotient is a perfect cube, we have to find the prime factors of 88209.
88209=3×3×3×3×3×3×11×11
Prime factors of 88209 are 3,3,3,3,3,3,11,11.
Out of the prime factors of 88209, 11 cannot be considered in its perfect cube as it have only two factors of 11.
So, 11×11 is the number by which 88209 must be divided to make the quotient a perfect cube.
⇒
11×11
88209
=729
3
729
=9
Hence, the smallest number is 121, which when divides 88209, the quotient is 729 which is a perfect cube.
Hence, the correct answer is 121.
10584. = 41
When you extract factor of 10584= 2×2×2×3×3×3×7×7. So, in manner to make any number a perfect cube you will need a triplet of prime factors and here 7 is only two times. So, when we divide 10584 by 49. you will get a perfect cube
Answer:
ANSWER
To find the smallest number by which 88209 must be divided so that the quotient is a perfect cube, we have to find the prime factors of 88209.
88209=3×3×3×3×3×3×11×11
Prime factors of 88209 are 3,3,3,3,3,3,11,11.
Out of the prime factors of 88209, 11 cannot be considered in its perfect cube as it have only two factors of 11.
So, 11×11 is the number by which 88209 must be divided to make the quotient a perfect cube.
⇒
11×11
88209
=729
3
729
=9
Hence, the smallest number is 121, which when divides 88209, the quotient is 729 which is a perfect cube.
Hence, the correct answer is 121.