# Find the smallest possible number by which 8788 must be multiplied to obtain a perfect cube.

Last updated date: 27th Mar 2023

•

Total views: 306.9k

•

Views today: 7.83k

Answer

Verified

306.9k+ views

Hint: To find the smallest number to be multiplied by 8788 to make it a perfect cube, write the prime factorization of the number 8788. Observe the terms needed to be multiplied to it to make it a perfect cube. Multiply all the numbers that are needed to be multiplied to get the smallest number needed to make 8788 a perfect cube.

Complete step-by-step answer:

We have to find the smallest number to be multiplied to 8788 to make it a perfect cube. To do so, we will write the prime factorization of the number 8788.

To write the prime factorization of any number, start by dividing the number by the first prime number, which is 2 and then continue to divide by 2 until you get a number which is not divisible by 2 (which means that you get a decimal or remainder on dividing the number by 2). Then start dividing the number by the next prime number which is 3. Continue dividing the number by 3 until you get a number which is not divisible by 3. Thus, continuing the process, keep dividing the numbers by series of prime numbers \[5,7,...\]until the only numbers left are prime numbers. Write the given number as a product of all the prime numbers (considering the fact to count each prime number as many times as it divides the given number) to get the prime factorization of the given number.

Thus, the prime factorization of 8788 is \[8788={{2}^{2}}\times {{13}^{3}}\].

We observe that \[{{13}^{3}}\] is already a perfect cube. So, to make 8788 a perfect cube, we need to make \[{{2}^{2}}\] a perfect cube. Thus, the smallest number by which we need to multiply \[{{2}^{2}}\] is 2.

Hence, to make 8788 a perfect cube, the smallest number by which we need to multiply it is 2.

Note: It is necessary to observe that we need the smallest possible number to make 8788 a perfect cube. We will get multiple answers if we don’t consider the fact that we need to find the smallest number. A perfect cube is a number that is the cube of an integer.

Complete step-by-step answer:

We have to find the smallest number to be multiplied to 8788 to make it a perfect cube. To do so, we will write the prime factorization of the number 8788.

To write the prime factorization of any number, start by dividing the number by the first prime number, which is 2 and then continue to divide by 2 until you get a number which is not divisible by 2 (which means that you get a decimal or remainder on dividing the number by 2). Then start dividing the number by the next prime number which is 3. Continue dividing the number by 3 until you get a number which is not divisible by 3. Thus, continuing the process, keep dividing the numbers by series of prime numbers \[5,7,...\]until the only numbers left are prime numbers. Write the given number as a product of all the prime numbers (considering the fact to count each prime number as many times as it divides the given number) to get the prime factorization of the given number.

Thus, the prime factorization of 8788 is \[8788={{2}^{2}}\times {{13}^{3}}\].

We observe that \[{{13}^{3}}\] is already a perfect cube. So, to make 8788 a perfect cube, we need to make \[{{2}^{2}}\] a perfect cube. Thus, the smallest number by which we need to multiply \[{{2}^{2}}\] is 2.

Hence, to make 8788 a perfect cube, the smallest number by which we need to multiply it is 2.

Note: It is necessary to observe that we need the smallest possible number to make 8788 a perfect cube. We will get multiple answers if we don’t consider the fact that we need to find the smallest number. A perfect cube is a number that is the cube of an integer.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?