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Factors of 360
Factors of 360 are the list of integers that we can split evenly into 360. There are overall 24 factors of 360, of which 2, 3 and 5 are its prime factors. The Prime Factorization of 360 is 2^{3} × 3^{2} × 5.
 Factors of 360: 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
 Negative Factors of 360: 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
 Prime Factors of 360: 2, 3, 5
 Prime Factorization of 360: 2 × 2 × 2 × 3 × 3 × 5 = 2^{3} × 3^{2} × 5
 Sum of Factors of 360: 1170
1.  What Are the Factors of 360? 
2.  How to Calculate the Factors of 360? 
3.  Factors of 360 by Prime Factorization 
4.  Factors of 360 in Pairs 
5.  FAQs on Factors of 360 
What Are the Factors of 360?
Factors of 360 are the numbers which, when multiplied together, give the product as 360.
For example, the product of 36 and 10 gives 360. Thus, they are the factors of 360.
We know that 360 is a composite number, therefore, it will have many other factors.
They can be listed as 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.
Explore factors using illustrations and interactive examples:
 Factors of 300: The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
 Factors of 24: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
 Factors of 36: The factors of 6 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
 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.
 Factors of 72: The factors of 72 are 1, 2, 3, 4, 6, 8, 9 12, 18, 24, 36, and 72
How To Calculate the Factors of 360?
Let's learn how to calculate the factors of 360.
 Step 1: Write down the number to be factored. Here the number is 360.
 Step 2: Find the two numbers whose product gives 360
360 can be written as a product of 36 and 10.
Similarly, you can calculate all the other factors. The factors of 360 can be listed as 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.
Factors of 360 by Prime Factorization
Prime factorization refers to the method to express a composite number as the product of its prime factors.
It is done using the following steps.
Step 1: Write the pair of factors which on multiplication gives the required number.
Step 2: Check whether each of the factors are prime or not.
 If both the numbers are prime, they can be multiplied as it is.
 If one among them is prime and the other one is composite, then the composite number is broken down into its factors.
 If both the numbers are composite, they can be broken down further into their factors.
Factors of 360 by prime factorization
Step 1: 360 can be factored as product of 36 and 10.
Step 2: On checking the factors 36 and 10, we can observe that 36 is not a prime number. It can be factored as a square of 6 and 6 can further be factored as a product of 2 and 3.
10 is not a prime number. Hence, it can be factored as 2 and 5.
360 can be written as 2 × 2 × 2 × 3 × 3 × 5.
Hence, the prime factors of 360 can be written as 360 = 2^{3} × 3^{2 }× 5
Now that we have done the prime factorization of our number, we can multiply the numbers and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.
Tips and Tricks
 1 is the smallest factor of every number. Hence, it is one among the factors of 360.
 360 is an even number, hence, it has 2 as one of its factors.
 The last digit of 360 is 0. Thus, it has 1, 2, 5 and 10 as its factors.
Factors of 360 in Pairs
The pair factors of 360 include a set of two numbers which, when multiplied together, give 360.
The positive pair factors of 360 can be listed as (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).
A number can have negative pair factors as well, because the product of two negative numbers gives a positive number.
The negative pair factors of 360 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).
Challenging Questions
 Can you think of the number of ways in which 360 plates can be stacked?
 Is 6 a factor of 360? If yes, state the reason.
Factors of 360 Solved Examples

Example 1: Three customers visited Cathy's boutique and bought some dresses. Can you help Cathy calculate the amount she earned per customer using the details given below? Is the amount calculated per customer a factor of 360?
Customer Number of dresses Cost of one dress 1 2 $180 2 1 $360 3 4 $90 Solution:
Customer Total cost of dresses 1 2 x $180 = $360 2 1 x $360 = $360 3 4 x $90 = $360 Yes, the amount calculated per customer is a factor of 360.

Example 2: Selena and Camilia went to a cafe. They paid $360 for the food they ate. If Selena paid $120, how much did Camilia pay? Was the amount paid by each one of them a factor of 360?
Solution:
The total amount paid by them was $360.
If Selena paid $120, then the amount paid by Camila was $360  $120 = $240
120 is a factor of 360, while 240 is not a factor of 360.
Hence, the amount paid by Selena is a factor of 360, while the amount paid by Camila is not a factor of 360.

Example 3: Find the product of all the prime factors of 360.
Solution:
Since, the prime factors of 360 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 360
What are the Factors 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, 60, 72, 90, 120, 180, 360 and its negative factors 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.
What are the Pair Factors of 360?
The pair factors of 360 are (1, 360), (2, 180), (3, 120), (4, 90), (5, 72), (6, 60), (8, 45), (9, 40), (10, 36), (12, 30), (15, 24), (18, 20).
What is the Sum of all the Factors of 360?
Sum of all factors of 360 = (2^{3 + 1}  1)/(2  1) × (3^{2 + 1}  1)/(3  1) × (5^{1 + 1}  1)/(5  1) = 1170
How Many Factors of 360 are also Factors of 252?
Since, 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 and the factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
Hence, [1, 2, 3, 4, 6, 9, 12, 18, 36] are the common factors of 360 and 252.
What is the Greatest Common Factor of 360 and 102?
The factors of 360 and 102 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 and 1, 2, 3, 6, 17, 34, 51, 102 respectively.
Common factors of 360 and 102 are [1, 2, 3, 6].
Hence, the Greatest Common Factor of 360 and 102 is 6.
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