Factors of 180 Using Prime Factorization
Factors of 180
Factors | Factor Pairs | Prime factorization |
|---|---|---|
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180 | (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6,30), (9, 20), (10, 18), (12, 15) | 180 = 2 × 2 × 3 × 3 × 5 |
What are the Factors of 180?
The factors of 180 are integers that divide 180 without leaving any remainder, or in other words, the factors of 180 are divisors of 180.
For example, 90 is a factor of 180 because when we divide 180 by 90, it gives us 2 as the quotient and 0 as the remainder. The quotient 2 is also a factor of 180.
So, to check if any number is a factor of 180, divide 180 by that number and check if the remainder is zero or not.
Factor List of 180
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 Factors of 180
The factor tree of 180 can be written as:
From the factor tree, we can see that the prime factorization of 180 is 2 \(\times\) 2 \(\times\) 3 \(\times\) 3 \(\times\) 5 = \( 2^2 ~\times~3^2~\times~5\).
This means 2, 3 and 5 are the prime factors of 180.
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Factor Pairs of 180
A factor pair of 180 is a set of two factors of 180 which when multiplied together result in 180.
For example, (2, 90) is a factor pair of 180 as both 2 and 90 are factors of 180 and 2 \(\times\) 90 = 180
Positive Factor Pairs of 180
Rapid Recall
Solved Factors on 180 Examples
Example 1: Find the common factors of 180 and 100.
Solution:
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100.
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.
So, the common factors of 180 and 100 are 1, 2, 4, 5, 10 and 20.
Example 2: How many factors does 180 have?
Solution:
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.
So, there are 18 factors of 180.
Example 3: John has 180 chocolates and Max has 120 chocolates. Find the greatest common divisor that can divide the number of chocolates that John has and the number of chocolates Max has completely.
Solution:
To find the greatest common divisor, we will have to first find the common factors of 180 and 120.
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.
The common factors of 120 and 180 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Therefore, the greatest common factor of 120 and 180 is 60.
When we divide 180 by 7, we are left with 5 as a remainder, that is, 7 does not divide 180 exactly. Hence, 7 is not a factor of 180.
Numbers that divide 180 exactly, which are numbers that leave no remainder on dividing 180 by it, are known as factors of 180.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180. Hence, the sum of all the factors of 180 is
= 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 30 + 36 + 45 + 60 + 90 + 180 = 546
Hence, the sum is 546.
Yes, 180 is a composite number as it has factors other than one and itself. It has factors of 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 and 90 other than 1 and 180.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180. So, the least factor of 180 is 1 and the greatest factor of 180 is 180 itself.