In Mathematics, numbers are the building blocks and their fundamental properties. One such property is factors of numbers. In this Math tutorial, we will study the **factors of 2**, how to calculate the factors of 2, and the prime factors of 2.

As we know, 2 is an even number and a prime number. Which means, it is divisible by itself.

All the even numbers are multiple and divisible by 2.

The number 2 is the smallest number and smallest prime number.

**Factors of 2: 1 and 2 **

**Prime Factors of 2: 2**

## What are the factors of 2?

When we talk about the factors of a number, we are referring to the whole numbers that can be multiplied together to give that number as a product. In the case of the number 2, its factors are simply 1 and 2 itself. Let’s understand it using an example:

Example 1: Let’s take the number as 4 and 4 is a multiple of 2. Its factors are 1, 2, and 4. In this case, 2 is a prime factor of 4

Example 2: Let’s take the number as 8 and 8 is yet another multiple of 2. Its factors are 1, 2, 4, and 8. In this case, 2 is both a factor and a prime factor, as it cannot be divided further into prime numbers.

**Note : **

- All the numbers except for 1 have at least 2 factors.
- The Prime factor of a prime number would always be the number itself.
- Even numbers will always have 2 as their factors.

**What Is a Factor of 2? | ****What Is the Prime Factorization of 2?**

A factor of 2 is any whole number that can be multiplied by another whole number to yield 2 as the result.

In the case of 2, the factors are 1 and 2, because 1 x 2 = 2.

We have only taken the positive integers in the article.

Let’s see the factors of other prime numbers:

- The factor of 3: 1 and 3
- Factors of 5: 1 and 5
- The factor of 7: 1 and 7

So, from the above factors of prime numbers, we have understood that the prime number has only two factors i.e. 1 and the number itself.

Likewise, we will cover a very important topic on prime factors. Prime factorization involves expressing a number as a product of prime numbers.

However, 2 is a prime number itself, which means it cannot be further broken down into a product of smaller prime numbers.

Therefore, the prime factorization of 2 is simply 2.

- Prime factor of 2: 2
- Prime factor of 3: 3
- Prime factor of 6: 2,3

Hence, the prime factor of the prime number would be the number itself.

## Why is it important to factorize a number?

Factors are one of the most important topics in Mathematics for various reasons :

**Divisibility:**If you understand factors then here is what it does. It helps determine whether one number is divisible by another. For example, if a number is divisible by 2, it means 2 is one of its factors.**Prime Numbers:**It is important to identify prime factors as it is essential for working with prime numbers and solving problems related to prime factorization. For example, if a number is 3 then, the prime factor for 3 would be 3.**Simplifying Fractions:**Usually, factors are used to simplify fractions in Math. When we know the common factors of the numerator and denominator it will help us to reduce fractions to their simplest form.

## How to calculate Factors of a Number?

Understanding factors helps determine whether one number is divisible by another.

For instance, if a number is divisible by 2, it means 2 is one of its factors. Also, to calculate the factor of a number we need to see the divisibility of that given number with the other numbers.

The factors of any number exist in Pairs. So, the Pair factor of 2 would be (1,2 ).

Let’s find out the factors of a few numbers and their pair factor.

Number | Pair factor | Factors of the number |

2 | (1, 2) | 1,2 |

3 | (1, 3) | 1,3 |

4 | (1, 2), (1, 4), (2, 4) | 1,2,4 |

5 | (1, 5) | 1,5 |

12 | (1, 12), (2, 6), (3, 4) | 1,2,3,4,6,12 |

15 | (1, 15), (3, 5) | 1, 3, 5, 15 |

28 | (1, 28), (2, 14), (4, 7) | 1, 2, 4, 7, 14, 28 |

37 | (1, 37) | 1, 37 |

56 | (1, 56), (2, 28), (4, 14), (7, 8) | 1, 2, 4, 7, 8, 14, 28, 56 |

99 | (1, 99), (3, 33), (9, 11) | 1, 3, 9, 11, 33, 99 |

100 | (1, 100), (2, 50), (4, 25), (5, 20), (10, 10) | 1, 2, 4, 5, 10, 20, 25, 50, 100 |

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