Integer Factorization Calculator

Welcome to the Integer Factorization Calculator – Factors, Factor Pairs, and Prime Factorization of a Number.

5 Uses of the Integer Factorization Calculator

1. It helps you easily find the factors of a number.
2. It helps you determine which multiplications produce a given number.
3. It helps you find the prime factors of a number.
4. It helps you find the prime factorization of a number, which is used to determine the LCM and GCD of two or more numbers.
5. It helps you determine whether a number is a prime number or not.

How the Integer Factorization Calculator Works

To understand how this calculator works, please read the following explanations.

Factors of a Number

The factors of a number are numbers that divide the given number evenly.

For example, the factors of 6 are 1, 2, 3, and 6 because 6 can be divided evenly by these numbers.

To determine whether a natural number $n$ is divisible by a natural number $p$, we simply need to find a natural number $q$ such that $n = p \times q$.

EXAMPLE 1: Is 6 a factor of 24?

This question is equivalent to asking whether 24 can be divided by 6. The answer is yes, because there exists a natural number 4 such that $24 = 6 \times 4$.

Therefore, 6 is a factor of 24.

EXAMPLE 2: Is 3 a factor of 10?

This question is equivalent to asking whether 10 can be divided by 3. The answer is no, because there is no natural number $q$ such that $10 = 3 \times q$.

Therefore, 3 is not a factor of 10.

Note: A natural number $n$ is divisible by $p$ if the remainder of the division is 0. If the remainder is not zero, then $n$ is not divisible by $p$.

EXAMPLE 3: What are the factors of 24?

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

Factor Pairs of a Number

Factor pairs of a natural number are two numbers that are factors of the number such that their product equals the given number.

EXAMPLE 1: What are the factor pairs of 24?

From the previous example, we know that 6 is a factor of 24 and 4 is also a factor of 24. Since $24 = 6 \times 4$, then 6 and 4 are a factor pair of 24.

In addition, 24 has other factor pairs, namely (1, 24), (2, 12), and (3, 8).

EXAMPLE 2: What multiplications result in 72?

The multiplications that result in 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9).

Prime Factors of a Number

The prime factors of a number are the factors of that number which are prime numbers.

EXAMPLE: What are the prime factors of 24?

From the previous examples, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these factors, the prime numbers are 2 and 3.

Therefore, the prime factors of 24 are 2 and 3.

Note: A prime number is a number greater than 1 that has exactly two factors, namely 1 and the number itself. Examples include 2, 3, 5, 7, 11, 13, and so on.

Prime Factorization of a Number

Prime factorization of a number is the multiplication of prime factors that represents the number.

EXAMPLE: What is the prime factorization of 24?

We can use a factor tree to determine the prime factorization of 24.

However, by knowing the factors of 24, we can determine its prime factorization as follows.

$\begin{align} 24 &= 6 \times 4 \\ &= (2 \times 3) \times (2 \times 2) \\ &= 2 \times 2 \times 2 \times 3 \\ &= 2^2 \times 3 \end{align}

Therefore, the prime factorization of 24 is $2^2 \times 3$.