Question

Find the smallest number by which 875 must be divided to obtain a perfect cube

Answer 1

SOLUTION

TO DETERMINE

The smallest number by which 875 must be divided to obtain a perfect cube

EVALUATION

Here the given number is 875

We know factorise 875

$\sf{875 = 5 \times 5 \times 5 \times 7}$

$\therefore \: \: \sf{875 = {5}^{3} \times 7}$

So 7 is the smallest number by which 875 must be divided to obtain a perfect cube

So that the obtained number is 125 is perfect cube

$\sf{( \: 125 = {5}^{3} \: ) }$

FINAL ANSWER

7 is the smallest number by which 875 must be divided to obtain a perfect cube

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Answer 2

Question -

Find the smallest number by which 875 must be divided to obtain a perfect cube

Answer -

Given that -

• Given number 875 that must be divided to obtain a perfect cube.

To find -

• Smallest number by 875 that must be divided to obtain a perfect cube.

Solution -

• 7 is the smallest number by 875 that must be divided to obtain a perfect cube.

Let's understand the concept 1st -

• This question says that we have to find a number but the smallest number by which 875 must be divided to obtain a perfect cube.

Procedure of this question -

• To solve this question firstly we have to prime factorize 875. After factorize it we get 7. Hence, easily we get our final result that is 7.

Full solution -

Finding prime factorization of 875 ➝

↝ 875 = 5 × 5 × 5 × 7

If we see it as in exponent form then ➝

↝ 875 = 5³ × 7

Hence, 7 is the smallest number by 875 that must be divided to obtain a perfect cube.

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Hence, we have done. But also let's see that number ( perfect cubed number ) !

As we get 5³ as in exponent form. Then let's the number now,

↝ 5³ means 5 × 5 × 5

↝ 5³ means 25 × 5

↝ 5³ means 125

Hence, 125 is the perfect cube in this question which 7 is the smallest number by 875 that must be divided to obtain a perfect cube.

More knowledge -

What is prime factorization ?

This is the decomposition of a composite number into a product of smaller integers.

What is prime number ?

A number that is divisible by itself and one is known to be prime number.

What is cube ?

In arithmetic and algebra, the cube of a number n is its third power.

What is cube root ?

Cube root is that number which produced a given number when cubed.