Factors of 12

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 12, which are mentioned below:

Negative factors of 12: -1, -2, -3, -4, -6, -12

Prime factors of 12:   2, and 3

Prime factorization of 12: 2² × 3¹

The sum of factors of 12: 1 + 2 + 3 + 4 + 6 + 12 = 28

For finding factors, school kids use different methods for easy calculation. A few commonly used methods are as follows:

• Use of Multiplication Method
• Use of Division Method
• Use of Prime Factors and Prime Factorization

So, here we 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 12. We will check the factors step by step:

Step 1: Start to multiply with numbers, which gives the value of 12.

Start with 1, and continue to multiply with other numbers. 

1 × 12 = 12
2 × 6 = 12
3 × 4 = 12

Step 2: After the calculation, we get these numbers, the factors of 12.

Step 3: The positive factor pairs of 12 found through multiplication are(1,12), (2,6), and (3,4)

Step 4: The negative factor pairs of 12 are (-1,-12), (-2,-6), and  (-3,-4)
 

Using this method, we will break down the given number till our remainder is zero. Let us go through the step-by-step process to find the factors of 108:

Step 1: Divide 108 by smaller numbers and see if there is any remainder. E.g., 108/1 = 108.

 
Step 2: We will continue in the same way and check for other numbers as well. For 108, the factors are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 and 108. Because 108 can be divided evenly by these numbers.
 

The prime factors of 108 are 2 and 3. 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 factor. 

2 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.

108 ÷ 2 = 54
54  ÷ 2 = 27
27 ÷ 3 = 9
9  ÷ 3 = 3
3  ÷ 3 = 1

 The prime factorization of 108 is :

 108 = 2² × 3³

Finally, using the prime factorization method, the prime factors of 108 are 2 and 3.
 

 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: 108 divided by 2 gives us the answer 54.

Step 2: Since 54 is not a prime number, it can be divided further.

108 ÷ 2 = 54
54  ÷ 2 = 27
27 ÷ 3 = 9
9  ÷ 3 = 3
3  ÷ 3 = 1 

The prime factorization of 108 is written below : 

  108 = 2² × 3³
 

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

Positive pair Factors:  (1,108), (2,54), (3,36), (4,27), (6,18), and (9,12)
Negative pair Factors: (-1,-108), (-2,-54), (-3,-36), (-4,-27), (-6,-18), and (-9,-12)
 

• 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 the numbers that multiply together to give a certain product. For 108, the prime factors are 2 and 3.

• 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).