Factors of 360 Using Prime Factorization
What are the Factors of 360?
We can find the factors of 360 by identifying the numbers that divide 360 evenly without leaving any remainder. As 360 is a composite number, it will have other factors apart from 1 and 360, as well.
List of Factors of 360
The table here shows the factors of 360 by applying divisibility rules and division facts.
Number | Is the number a factor of 360? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 360 = 360 |
2 | Yes, 360 \( \div\) 2 = 180 Remainder = 0 | 2 x 180 = 360 |
3 | Yes, 360 \( \div\) 3 = 120 Remainder = 0 | 3 x 120 = 360 |
4 | Yes, 360 \( \div\) 4 = 90 Remainder = 0 | 4 x 90 = 360 |
5 | Yes, 360 \( \div\) 5 = 72 Remainder = 0 | 5 x 72 = 360 |
6 | Yes, 360 \( \div\) 6 = 60 Remainder = 0 | 6 x 60 = 360 |
7 | No, 360 \( \div\) 7 = 51 Remainder = 3 | - |
8 | Yes, 360 \( \div\) 8 = 45 Remainder = 0 | 8 x 45 = 360 |
9 | Yes, 360 \( \div\) 9 = 40 Remainder = 0 | 9 x 40 = 360 |
10 | Yes, 360 \( \div\) 10 = 36 Remainder = 0 | 10 x 36 = 360 |
11 | No, 360 \( \div\) 11 = 32 Remainder = 8 | - |
12 | Yes, 360 \( \div\) 12 = 30 Remainder = 0 | 12 x 30 = 360 |
13 | No, 360 \( \div\) 13 = 27 Remainder = 9 | - |
14 | No, 360 \( \div\) 14 = 25 Remainder = 10 | - |
15 | Yes, 360 \( \div\) 15 = 24 Remainder = 0 | 15 x 24 = 360 |
16 | No, 360 \( \div\) 16 = 22 Remainder = 8 | - |
17 | No, 360 \( \div\) 17 = 21 Remainder = 3 | - |
18 | Yes, 360 \( \div\) 18 = 20 Remainder = 0 | 18 x 20 = 360 |
19 | No, 360 \( \div\) 19 = 18 Remainder = 18 | - |
20 | Yes, 360 \( \div\) 20 = 3 Remainder = 0 | 20 x 18 = 360 |
As we can observe in the table, as we progress beyond the division and multiplication operations of the number 20, the factor pairs will start to repeat. Hence, we can conclude here, and say that the factors of 360 are, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.
Prime Factors of 360
By applying the factor tree method it’s convenient to list the prime factors of 360.
The image shows that the prime factors of 360 are,
360 = 2 x 2 x 2 x 3 x 3 x 5
Hence, the prime factors of 360 are 2,3 and 5.
Factor Pairs of 360
When a particular pair of numbers are multiplied and result in the original number as the product, then these pairs of numbers are called factor pairs. The factor pairs of 360 are:
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Rapid Recall
Solved Factors of 360 Examples
Example 1:
Charlie and Shawn visited a restaurant. The food they had cost them $360. How much did Shawn pay if Charlie paid $90? Was the sum each of them paid a factor of 360?
Solution:
As mentioned, the total amount paid by both Shawn and Charlie was $360.
If Charlie paid $90, then, the amount paid by Shawn would be,
$360 – $90 = $270
Hence, Shawn needs to pay $270.
360 \(\div\) 90 = 4 R0
360 \(\div\) 270 = 1 R90
So, 90 is a factor of 360, but 270 is not a factor of 360.
Example 2:
What is the greatest common factor of the numbers 360 and 400?
Solution:
The factors of 400 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200 and 400.
And the factors of 360 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360.
From the list of factors, the greatest common factor of 360 and 400 is 40.
Example 3:
What would be the product of prime factors of the number 360?
Solution:
As we know, the prime factors of 360 are 2, 3 and 5
⇒ 2 × 3 × 5
⇒ 30
Hence, the product of prime factors of 360 is 30.
Since the prime factors of 360 are 2³×3²×5, two appears three times in the prime factorization of 360.
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 72, 90, 120, 180, 360.
Adding all these factors together, the sum is,
⇒ 1 +2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 72 + 90 + 120 + 180 + 360 = 1170
By adding up all the factors of 360, the sum will be 1170.
No, 360 is not a prime number as it has 24 factors. This proves that 360 is a composite number.
There are 12 factor pairs of 360. They are (1, 360), (2, 180), (3, 120), (4, 90), (5, 72), (6, 60), (8, 45), (9, 40), (10, 36), (12, 30), (15, 24), and (18, 20).