Finding the Smallest Number to Make a Perfect 6

Oct 13, 2025 by talynt.org 31 views

Finding the Smallest Number to Make a Perfect 6 and a Perfect Cube

In mathematics, finding the smallest number to make a perfect 6 or a perfect cube is an essential concept in number theory. A perfect 6 is a number that is divisible by 6, while a perfect cube is a number that can be expressed as the cube of an integer. In this article, we will explore the concept of finding the smallest number to make a perfect 6 and a perfect cube.

Finding the Smallest Number to Make a Perfect 6

To find the smallest number by which 14739 must be multiplied so that the product is a perfect 6, we need to analyze the prime factorization of 14739.

Prime Factorization of 14739

The prime factorization of 14739 is:

14739 = 3 × 4913

Since 14739 is not divisible by 6, we need to find the smallest number that, when multiplied by 14739, will result in a product that is divisible by 6.

Finding the Smallest Number

To find the smallest number, we need to analyze the prime factorization of 6, which is:

6 = 2 × 3

Since 14739 is already divisible by 3, we need to find the smallest number that, when multiplied by 14739, will result in a product that is divisible by 2.

Smallest Number to Make a Perfect 6

The smallest number that, when multiplied by 14739, will result in a product that is divisible by 2 is 2 itself. Therefore, the smallest number by which 14739 must be multiplied so that the product is a perfect 6 is 2.

Finding the Smallest Number to Make a Perfect Cube

To find the smallest number by which 1375 must be divided so that the quotient is a perfect cube, we need to analyze the prime factorization of 1375.

Prime Factorization of 1375

The prime factorization of 1375 is:

1375 = 5^3 × 11

Since 1375 is not a perfect cube, we need to find the smallest number that, when divided by 1375, will result in a quotient that is a perfect cube.

Finding the Smallest Number

To find the smallest number, we need to analyze the prime factorization of the perfect cube, which is 11^3.

Smallest Number to Make a Perfect Cube

The smallest number that, when divided by 1375, will result in a quotient that is a perfect cube is 11^2, which is 121. Therefore, the smallest number by which 1375 must be divided so that the quotient is a perfect cube is 121.

Cube Root of a Number

The cube root of a number x is a number that, when cubed, gives the original number x. In other words, it is the number that, when multiplied by itself three times, gives the original number.

Properties of Cube Root

The cube root of a number has the following properties:

It is a number that, when cubed, gives the original number.
It is a number that, when multiplied by itself three times, gives the original number.
It is a number that, when raised to the power of 1/3, gives the original number.

Examples of Cube Root

Some examples of cube root include:

The cube root of 27 is 3, because 3^3 = 27.
The cube root of 64 is 4, because 4^3 = 64.
The cube root of 125 is 5, because 5^3 = 125.

In our previous article, we discussed the concept of finding the smallest number to make a perfect 6 and a perfect cube. In this article, we will answer some frequently asked questions related to cube root and perfect numbers.

Q: What is the cube root of a number?

A: The cube root of a number x is a number that, when cubed, gives the original number x. In other words, it is the number that, when multiplied by itself three times, gives the original number.

Q: How do I find the cube root of a number?

A: To find the cube root of a number, you can use the following methods:

Use a calculator: Most calculators have a cube root function that you can use to find the cube root of a number.
Use a formula: The cube root of a number x can be found using the formula: x^(1/3) = ∛x.
Use a table: You can use a table of cube roots to find the cube root of a number.

Q: What is a perfect cube?

A: A perfect cube is a number that can be expressed as the cube of an integer. In other words, it is a number that can be written in the form: n^3, where n is an integer.

Q: How do I find the smallest number to make a perfect cube?

A: To find the smallest number to make a perfect cube, you need to analyze the prime factorization of the number. If the number is not a perfect cube, you need to find the smallest number that, when multiplied by the number, will result in a product that is a perfect cube.

Q: What is the smallest number to make a perfect 6?

A: The smallest number to make a perfect 6 is 2. This is because 2 is the smallest number that, when multiplied by 14739, will result in a product that is divisible by 6.

Q: What is the smallest number to make a perfect cube?

A: The smallest number to make a perfect cube is 11^2, which is 121. This is because 121 is the smallest number that, when divided by 1375, will result in a quotient that is a perfect cube.

Q: Can you give some examples of cube root?

A: Yes, here are some examples of cube root:

The cube root of 27 is 3, because 3^3 = 27.
The cube root of 64 is 4, because 4^3 = 64.
The cube root of 125 is 5, because 5^3 = 125.

Q: Can you give some examples of perfect cubes?

A: Yes, here are some examples of perfect cubes:

1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125

In conclusion, finding the cube root and perfect numbers is an essential concept in number theory. By understanding the properties of cube root and perfect numbers, we can find the smallest number to make a perfect 6 and a perfect cube. We hope that this article has answered some of your frequently asked questions related to cube root and perfect numbers.