Factors of 4320
Factors of 4320 are integers that can be divided evenly into 4320. There are overall 48 factors of 4320 among which 4320 is the biggest factor and its prime factors are 2, 3, 5. The Prime Factorization of 4320 is 25 × 33 × 51.
- All Factors of 4320: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160 and 4320
- Prime Factors of 4320: 2, 3, 5
- Prime Factorization of 4320: 25 × 33 × 51
- Sum of Factors of 4320: 15120
1. | What Are the Factors of 4320? |
2. | Factors of 4320 by Prime Factorization |
3. | Factors of 4320 in Pairs |
4. | FAQs on Factors of 4320 |
What are Factors of 4320?
Factors of 4320 are pairs of those numbers whose products result in 4320. These factors are either prime numbers or composite numbers.
How to Find the Factors of 4320?
To find the factors of 4320, we will have to find the list of numbers that would divide 4320 without leaving any remainder.
- 4320/48 = 90; therefore, 48 is a factor of 4320 and 90 is also a factor of 4320.
- 4320/3 = 1440; therefore, 3 is a factor of 4320 and 1440 is also a factor of 4320.
☛ Also Check:
- Factors of 27 - The factors of 27 are 1, 3, 9, 27
- Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 121 - The factors of 121 are 1, 11, 121
- Factors of 100 - The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
- Factors of 38 - The factors of 38 are 1, 2, 19, 38
Factors of 4320 by Prime Factorization
- 4320 ÷ 2 = 2160
- 2160 ÷ 2 = 1080
- 1080 ÷ 2 = 540
- 540 ÷ 2 = 270
- 270 ÷ 2 = 135
Further dividing 135 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 135 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.
So, the prime factorization of 4320 can be written as 25 × 33 × 51 where 2, 3, 5 are prime.
Factors of 4320 in Pairs
Pair factors of 4320 are the pairs of numbers that when multiplied give the product 4320. The factors of 4320 in pairs are:
- 1 × 4320 = (1, 4320)
- 2 × 2160 = (2, 2160)
- 3 × 1440 = (3, 1440)
- 4 × 1080 = (4, 1080)
- 5 × 864 = (5, 864)
- 6 × 720 = (6, 720)
- 8 × 540 = (8, 540)
- 9 × 480 = (9, 480)
- 10 × 432 = (10, 432)
- 12 × 360 = (12, 360)
- 15 × 288 = (15, 288)
- 16 × 270 = (16, 270)
- 18 × 240 = (18, 240)
- 20 × 216 = (20, 216)
- 24 × 180 = (24, 180)
- 27 × 160 = (27, 160)
- 30 × 144 = (30, 144)
- 32 × 135 = (32, 135)
- 36 × 120 = (36, 120)
- 40 × 108 = (40, 108)
- 45 × 96 = (45, 96)
- 48 × 90 = (48, 90)
- 54 × 80 = (54, 80)
- 60 × 72 = (60, 72)
Negative pair factors of 4320 are:
- -1 × -4320 = (-1, -4320)
- -2 × -2160 = (-2, -2160)
- -3 × -1440 = (-3, -1440)
- -4 × -1080 = (-4, -1080)
- -5 × -864 = (-5, -864)
- -6 × -720 = (-6, -720)
- -8 × -540 = (-8, -540)
- -9 × -480 = (-9, -480)
- -10 × -432 = (-10, -432)
- -12 × -360 = (-12, -360)
- -15 × -288 = (-15, -288)
- -16 × -270 = (-16, -270)
- -18 × -240 = (-18, -240)
- -20 × -216 = (-20, -216)
- -24 × -180 = (-24, -180)
- -27 × -160 = (-27, -160)
- -30 × -144 = (-30, -144)
- -32 × -135 = (-32, -135)
- -36 × -120 = (-36, -120)
- -40 × -108 = (-40, -108)
- -45 × -96 = (-45, -96)
- -48 × -90 = (-48, -90)
- -54 × -80 = (-54, -80)
- -60 × -72 = (-60, -72)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 4320 Solved Examples
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Example 1: How many factors are there for 4320?
Solution:
The factors of 4320 are too many, therefore if we can find the prime factorization of 4320, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).
Prime Factorization of 4320 = 25 × 33 × 51
Therefore, the total number of factors are (5 + 1) × (3 + 1) × (1 + 1) = 6 × 4 × 2 = 48 -
Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 4320 and 301.
Solution:
The factors of 4320 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160, 4320 and factors of 301 are 1, 7, 43, 301.
Therefore, the Least Common Multiple of 4320 and 301 is 1300320 and Highest Common Factor (HCF) of 4320 and 301 is 1. -
Example 3: Find if 6, 27, 45, 120, 240, 360, 432 and 1837 are factors of 4320.
Solution:
When we divide 4320 by 1837 it leaves a remainder. Therefore, the number 1837 is not a factor of 4320. All numbers except 1837 are factors of 4320.
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Example 4: Find the product of all the prime factors of 4320.
Solution:
Since, the prime factors of 4320 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 4320
What are the Factors of 4320?
The factors of 4320 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160, 4320 and its negative factors are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -27, -30, -32, -36, -40, -45, -48, -54, -60, -72, -80, -90, -96, -108, -120, -135, -144, -160, -180, -216, -240, -270, -288, -360, -432, -480, -540, -720, -864, -1080, -1440, -2160, -4320.
What is the Sum of all Factors of 4320?
Sum of all factors of 4320 = (25 + 1 - 1)/(2 - 1) × (33 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) = 15120
What are Pair Factors of 4320?
The pair factors of 4320 are (1, 4320), (2, 2160), (3, 1440), (4, 1080), (5, 864), (6, 720), (8, 540), (9, 480), (10, 432), (12, 360), (15, 288), (16, 270), (18, 240), (20, 216), (24, 180), (27, 160), (30, 144), (32, 135), (36, 120), (40, 108), (45, 96), (48, 90), (54, 80), (60, 72).
What is the Greatest Common Factor of 4320 and 4129?
The factors of 4320 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160, 4320 and the factors of 4129 are 1, 4129. 4320 and 4129 have only one common factor which is 1. This implies that 4320 and 4129 are co-prime.
Hence, the Greatest Common Factor (GCF) of 4320 and 4129 is 1.
How Many Factors of 4320 are also common to the Factors of 1432?
Since, the factors of 4320 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160, 4320 and the factors of 1432 are 1, 2, 4, 8, 179, 358, 716, 1432.
Hence, [1, 2, 4, 8] are the common factors of 4320 and 1432.
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