The factors of 180 are the numbers that divide 180 exactly without leaving a remainder. The factors and the pair factors of 180 can be represented in both positive and negative forms. For example, the factors of 180 can be expressed as (1, 180) or (-1, -180). If we multiply a pair of negative factors, such as multiplying -1 and -180, it will result in the original number 180.
Here, we are going to discuss the factors of 180, pair factors and the prime factors of 180 using the prime factorization method and many solved examples.
Table of Contents:
- What are the Factors of 180?
- Pair Factors of 180
- Factors of 180 by Division Method
- Prime Factorization of 180
- Solved Examples
- FAQs
What are the Factors of 180?
The numbers that divide 180 completely and leave a remainder value of 0 are the factors of 180. In other words, the numbers multiplied in pairs resulting in 180 are the factors of 180. As 180 is an even composite number, it has many factors other than 1 and 180. Hence, the factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180. Similarly, the negative factors of 180 are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -60, -90 and -180.
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.
Prime Factorization of 180: 2 × 2 × 3 × 3 × 5 or 22 × 32 × 5.
Pair Factors of 180
A pair of numbers that are multiplied together resulting in 180 are the pair factors of 180. As the number 180 is a composite number, it has more than one pair factors. The positive and negative pair factors of 180 are given below:
Positive Pair Factors of 180:
Positive Factors of 180
Positive Pair Factors of 180
1 × 180
(1, 180)
2 × 90
(2, 90)
3 × 60
(3, 60)
4 × 45
(4, 45)
5 × 36
(5, 36)
6 × 30
(6, 30)
9 × 20
(9, 20)
10 × 18
(10, 18)
12 × 15
(12, 15)
Therefore, the positive pair factors of 180 are (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), (10, 18) and (12, 15).
Negative Pair Factors of 180:
Negative Factors of 180
Negative Pair Factors of 180
-1 × -180
(-1, -180)
-2 × -90
(-2, -90)
-3 × -60
(-3, -60)
-4 × -45
(-4, -45)
-5 × -36
(-5, -36)
-6 × -30
(-6, -30)
-9 × -20
(-9, -20)
-10 × -18
(-10, -18)
-12 × -15
(-12, -15)
Therefore, the negative pair factors of 180 are (-1, -180), (-2, -90), (-3, -60), (-4, -45), (-5, -36), (-6, -30), (-9, -20), (-10, -18) and (-12, -15).
Factors of 180 by Division Method
If the integers divide 180 and leave a remainder value 0, then the integers are the factors of 180. The division method to find the factors of 180 are given below:
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Start dividing 180 by 1 and continue with the different integer values.
- 180/1 = 180 (Factor is 1 and Remainder is 0)
- 180/2 = 90 (Factor is 2 and Remainder is 0)
- 180/3 = 60 (Factor is 3 and Remainder is 0)
- 180/4 = 45 (Factor is 4 and Remainder is 0)
- 180/5 = 36 (Factor is 5 and Remainder is 0)
- 180/6 = 30 (Factor is 6 and Remainder is 0)
- 180/9 = 20 (Factor is 9 and Remainder is 0)
- 180/10 = 18 (Factor is 10 and Remainder is 0)
- 180/12 = 15 (Factor is 12 and Remainder is 0)
- 180/15 = 12 (Factor is 15 and Remainder is 0)
- 180/18 = 10 (Factor is 18 and Remainder is 0)
- 180/20 = 9 (Factor is 20 and Remainder is 0)
- 180/30 = 6 (Factor is 30 and Remainder is 0)
- 180/36 =5 (Factor is 36 and Remainder is 0)
- 180/45 = 4 (Factor is 45 and Remainder is 0)
- 180/60 = 3 (Factor is 60 and Remainder is 0)
- 180/90 = 2 (Factor is 90 and Remainder is 0)
- 180/180 = 1 (Factor is 180 and Remainder is 0)
If we divide 180 by any numbers other than 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180, it leaves a remainder. Hence, the factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.
Prime Factorization of 180
The process of writing the number 180 as the product of its prime factors is called the prime factorization of 180. Now, let us discuss how to find the prime factors of 180 using the prime factorization method.
Take the pair factor of 180, say (1, 180)
Here, the number 180 is a composite number, which can be further factored into its prime factors.
Thus, 180 is written as 4 × 45, which is equal to 4 × 9 × 5
Now, 5 is a prime number, but 4 and 9 are still composite numbers. So, we can further split the numbers into their prime factors.
Thus, 180 is written as 2 × 2 × 3 × 3 × 5.
Hence, the prime factorization of 180 is 2 × 2 × 3 × 3 × 5 or 22 × 32 × 5.
Video Lesson on Prime Factors
Solved Examples
Example 1:
Find the common factors of 180 and 179.
Solution:
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
The factors of 179 are 1 and 179.
As 179 is a prime number, the common factor of 180 and 179 is 1.
Example 2:
Find the common factors of 180 and 181.
Solution:
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
Factors of 181 = 1 and 181.
The common factor of 180 and 181 is 1 only, as 181 is a prime number.
Example 3:
Find the common factors of 180 and 90.
Solution:
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
Hence, the common factors of 180 and 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
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