Factors of 14

Factors often come in pairs. There are several methods to figure them out, which you'll be learning about in a second. For now, let's just focus on the factors of 14, which are mentioned below:

Negative factors of 14: -1, -2, -7, -14
Prime factors of 14: 2 and 7
Prime factorization of 14: 2 × 7
The sum of factors of 14: 1 + 2 + 7 + 14 = 24
 

To find factors, students typically use different methods for easier calculations. A few commonly used methods are as follows:

• The Multiplication Method
• The Division Method
• Prime Factorization (Prime Factor Method).

In this section, we will discuss a detailed explanation of the following methods:
 

In the multiplication method, we will try to find out what numbers will multiply together, and give us the value 14. We will check the factors step by step:

Step 1: Start by multiplying numbers to find those that give the value 14.

1 × 14 = 14
2 × 7 = 14

Step 2: These are the factors of 14.

Step 3: The positive factor pairs of 14 are (1, 14) and (2, 7).

Step 4: The negative factor pairs of 14 are (-1, -14) and (-2, -7).
 

Using this method, we will divide 14 by whole numbers and write down those numbers that leave no remainder. Let us go through the step-by-step process to find the factors of 14:

Step 1: Divide 14 by integers starting from 1 and check if there is any remainder. For example, 14 ÷ 1 = 14.

Step 2: Continue this process with other integers. For 14, the factors are 1, 2, 7, and 14. 14 can be evenly divided by these numbers.
 

The prime factors of 14 are 2 and 7. The prime factors can be found using the methods given below:

• Prime Factorization
• Factor Tree

By Using Prime Factorization:  It is a method in which we break down a number into its prime factors.

2 is the smallest prime number, so start by dividing by 2. Continue dividing by other prime numbers if needed.

14 ÷ 2 = 7
7 ÷ 7 = 1

The prime factorization of 14 is:

14 = 2 × 7

Through prime factorization, 14 can be broken down into its prime factors, which are 2 and 7.
 

A factor tree is a visual representation of breaking a number into its prime factors. It is an easy and simple way to present the factors.

Step 1: 14 divided by 2 gives us the quotient 7.

Step 2: Since 7 is a prime number, it cannot be divided further.

The prime factorization of 14 is written below:

14 = 2 × 7
 

Every number has either a positive or negative factor. Let us look at those sets of factors.

Positive pair Factors: (1,14), (2,7)
Negative pair Factors:  (-1,-14), (-2,-7)
 

• Factors:  Factors are numbers that divide a given number exactly, without any remainder. For example, 6 is divisible by 1, 2, 3, and 6. Therefore, 1, 2, 3, and 6 are the factors of 6.

• Prime Factors: Prime factors of a number are a set of prime numbers that multiply together to give the original number.  For 14, the prime factors are 2 and 7.

• Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).