In Mathematics, factors of 360 are the natural numbers (also called divisors), that exactly divide the original number. Since, 360 is a highly composite number, therefore the number of factors is more for 360.
The product of factors of 360, results in the original number, when multiplied in a particular pair. For example, 1 x 360 = 360. Such factors are called pair factors of 360. Let us find here all the factors, pair factors and prime factors of the number 360.
Factors | Pair Factors | Prime Factors Form |
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 | (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) | 2^{3} × 3^{2} × 5 |
How to Find the Factors of 360?
The factors of 360 can be evaluated when 360 is divisible by the natural numbers, completely.
- 360 ÷ 1 = 360
- 360 ÷ 2 = 180
- 360 ÷ 3 = 120
- 360 ÷ 4 = 90
- 360 ÷ 5 = 72
- 360 ÷ 6 = 60
- 360 ÷ 8 = 45
- 360 ÷ 9 = 40
- 360 ÷ 10 = 36
- 360 ÷ 12 = 30
- 360 ÷ 15 = 24
- 360 ÷ 18 = 20
Again, if we go in reverse order, then,
- 360 ÷ 20 = 18
- 360 ÷ 24 = 15
- 360 ÷ 30 = 12
- 360 ÷ 36 = 10
- 360 ÷ 40 = 9
- 360 ÷ 45 = 8
- 360 ÷ 60 = 6
- 360 ÷ 72 = 5
- 360 ÷ 90 = 4
- 360 ÷ 120 = 3
- 360 ÷ 180 = 2
- 360 ÷ 360 = 1
Therefore, we can conclude the factors of 360, i.e., 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.
More Factors
Pair Factors of 360
The pair factors are the pair of values that results in the original number (i.e. 360), on multiplication.
- 1 × 360 = 360
- 2 × 180 = 360
- 3 × 120 = 360
- 4 × 90 = 360
- 5 × 72 = 360
- 6 × 60 = 360
- 8 × 45 = 360
- 9 × 40 = 360
- 10 × 36 = 360
- 12 × 30 = 360
- 15 × 24 = 360
- 18 × 20 = 360
Therefore, 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), and (18, 20).
The product of two negative integers will result in a positive value. Therefore, we can consider pair of negative factors as well:
- -1 × -360 = 360
- -2 × -180 = 360
- -3 × -120 = 360
- -4 × -90 = 360
- -5 × -72 = 360
- -6 × -60 = 360
- -8 × -45 = 360
- -9 × -40 = 360
- -10 × -36 = 360
- -12 × -30 = 360
- -15 × -24 = 360
- -18 × -20 = 360
Therefore, the negative pair factors 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).
Prime Factorisation of 360
Prime factorisation of 360 will result in the product of prime numbers that will be equal to the original number. Hence, these prime numbers are the prime factors of 360, that divides it evenly.
Dividing 360 by smallest prime number, i.e.2 | 360 ÷ 2 = 180 |
180 is again divisible by 2 | 180 ÷ 2 = 90 |
90 is divisible by 2 | 90 ÷ 2 = 45 |
45 is divisible by prime number 3 | 45 ÷ 3 = 15 |
15 is divisible by 3 | 15 ÷ 3 = 5 |
5 is a prime number and divisible by itself | 5 ÷ 5 |
Therefore, the prime factors of 360 are 2, 3 and 5.
Prime factorisation of 360 = 2 x 2 x 2 x 3 x 3 x 5
Exponential form = 2^{3} × 3^{2} × 5 |
Solved Examples
Q.1: What is the value of 360 divided by 36?
Solution: 360 divided by 36 is:
360 ÷ 36 = 10
Therefore, the value of 360 divided by 36 is 10.
Q.2: What is the greatest common factor of 300 and 360?
Solution: Let us list the factors of both the numbers 300 and 360.
360 → 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
300 → 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Therefore, the greatest common factor of 360 and 300 is 60.
Q.3: Find the common factors of 250 and 360.
Solution: The factors are:
250 → 1, 2, 5, 10, 25, 50, 125, 250
360 → 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Therefore, the common factors of 250 and 360 are 1, 2, 5, 10.
Practice Questions
- How many factors are there for number 360?
- How can we divide 360 into 8 equal parts?
- Find if 7 is a factor of 360 or not.
- What is the GCF of 360 and 380?
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Frequently Asked Questions 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.
How many prime factors are there for 360?
The prime factorisation of 360 is equal to 2^{3} x 3^{2} x 5. Therefore, there are three prime factors of 360.
What are the multiples of 360?
The first ten multiples of 360 are 360, 720, 1080, 1440, 1800, 2160, 2520, 2880, 3240, 3600.
What is the highest factor of 360 apart from itself?
The highest factor of 360 apart from itself is 180.
What is the GCF of 64 and 360?
Answer: The GCF of 64 and 360 is 8. By prime factorisation,
64 = 2 × 2 × 2 × 2 × 2 × 2
360 = 2 × 2 × 2 × 3 × 3 × 5
GCF (64, 360) = 2 × 2 × 2 = 8