What are all the factors, the prime factorization, and factor pairs of 180?

Factors are essential building blocks in mathematics. They are the numbers you can multiply together to get another number. Taking 180 as an illustrative example, factors give insight into the composition and characteristics of 180, revealing its role in various mathematical contexts.

The factors of 180 are the set of integers that can be multiplied in pairs to equal 180. Below is a visual representation of these factors and their corresponding pairs in the multiplication process:

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

The factors of a number, such as 180, can be discovered using the division method. This involves dividing 180 by integers to identify which ones result in whole numbers, signifying that they are factors of 180. The process is visually demonstrated below:

Starting with 1, which is a factor of every natural number, and proceeding to divide 180 by other integers:

• 180 ÷ 1 = 180
• 180 ÷ 2 = 90
• 180 ÷ 3 = 60
• 180 ÷ 4 = 45
• 180 ÷ 5 = 36
• … and so on until 180 itself to get 1.

This process yields the entire set of factors for 180.

Pair factors of 180 consist of two numbers that, when multiplied, equate to 180. This includes both positive and negative pairs, as a negative times a negative yields a positive result. Below are listed pair factors of 180:

Breaking down 180 into prime factors requires dividing it by the smallest prime number until only 1 remains. Below is a factor tree diagram illustrating this process:

The prime factorization of 180 is 2 x 2 x 3 x 3 x 5, which can also be written as 2² x 3² x 5.

Here are key takeaways regarding the factors of 180:

• There are a total of 18 factors of 180.
• The prime factors of 180 are 2, 3, and 5.
• Pair factors include (1, 180), (2, 90), (3, 60), and so on.
• The sum of all factors of 180 is 546.