Factors of 180

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 180, which are mentioned below:

Negative factors of 180: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -60, -90, -180
Prime factors of 180:  2, 3, and 5
Prime factorization of 180: 22 × 32 × 51
The sum of factors of 180: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 30 + 36 + 45 + 60 + 90 + 180 = 546
 

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:
 

So in the multiplication method, we will try to find out what numbers will multiply together, and give us the value 180. We will check the factors step by step:

Step 1: Start to multiply with numbers, which gives the value of 180.

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

1 × 180 = 180
2  ×  90 = 180
3  ×  60 = 180
4  ×  45 = 180
5  ×  36 = 180
6  × 30 = 180
9  × 20 = 180
10  × 18 = 180
12  × 15 = 180

Step 2: After the calculation, we get the factors of 180.

Step 3: The positive factor pairs of 180 found through multiplication are(1,180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), (10, 18), (12, 15)

Step 4: The negative factor pairs of 180 are (-1,-180), (-2, -90), (-3, -60), (-4, -45), (-5, -36), (-6, -30), (-9, -20), (-10, -18), (-12, -15)
 

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 180:

Step 1: Divide 180 by smaller numbers and see if there is any remainder. E.g., 180/1 = 180. 

Step 2: We will continue in the same way and check for other numbers as well. For 180, the factors are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180. Because 180 can be divided evenly by these numbers.
 

The prime factors of 180 are 2, 3, and 5. 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 dividing with two. And then continue to divide with other prime numbers.

180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

 The prime factorization of 180 is :

 180 = 2² × 3² × 5¹

With prime factorization, 180 can be broken down into prime factors, 2, 3, and 5.

A factor tree is a graphical representation of breaking a composite number into its prime factors. It is an easy method to find out the factors of any number.

Step 1: 180 divided by 2 gives us the quotient 90.

Step 2: Since 90 is not a prime number, it can be divided further.

 The prime factorization of 180 is written below : 

180 = 2² × 3² × 5¹
 

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

Positive pair Factors: (1,180), (2,90), (3,60), (4,45), (5,36), (6,30), (9,20), (10,18), (12,15)
Negative pair Factors: (-1,-180), (-2,-90), (-3,-60), (-4,-45), (-5,-36), (-6,-30), (-9,-20), (-10,-18), (-12,-15)
 

• 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 180, the prime factors are 2, 3, and 5.

• 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).