Question

Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube. *

Answer 1

Answer:

answer is 25

Step-by-step explanation:

if we take l.c.m. of 2560 we'll get nine 2' a and the left over one is number 5 so 5*5 is 25 and if we multiply 25 and 2560 we'll get 64000 which is a perfect cube

Answer 2

Factorization is the process of simplifying the number based on its factors or divisors.

Now, we need to find the smallest number by applying the factorization to the given number.

Now, by factorizing the given number, we get,

\therefore 2560=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5=2^{9} \times 5∴2560=2×2×2×2×2×2×2×2×2×5=2

9

×5

The nearest perfect cube is obtained by multiplying 2^{9} \text { and } 5^{3}2

9

and 5

3

Therefore, the nearest perfect cube of 2^{9} \times 5=2^{9} \times 5^{3}2

9

×5=2

9

×5

3

Hence, the smallest number to be multiplied is 5^{2}=255

2

=25

ans. = smallest number is 25