Factors of 5400
Factors of 5400 are integers that can be divided evenly into 5400. There are 48 factors of 5400 of which 5400 itself is the biggest factor and its prime factors are 2, 3, 5 The sum of all factors of 5400 is 18600.
- All Factors of 5400: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700 and 5400
- Prime Factors of 5400: 2, 3, 5
- Prime Factorization of 5400: 23 × 33 × 52
- Sum of Factors of 5400: 18600
1. | What Are the Factors of 5400? |
2. | Factors of 5400 by Prime Factorization |
3. | Factors of 5400 in Pairs |
4. | FAQs on Factors of 5400 |
What are Factors of 5400?
Factors of 5400 are pairs of those numbers whose products result in 5400. These factors are either prime numbers or composite numbers.
How to Find the Factors of 5400?
To find the factors of 5400, we will have to find the list of numbers that would divide 5400 without leaving any remainder.
- 5400/1350 = 4; therefore, 1350 is a factor of 5400 and 4 is also a factor of 5400.
- 5400/6 = 900; therefore, 6 is a factor of 5400 and 900 is also a factor of 5400.
☛ Also Check:
- Factors of 55 - The factors of 55 are 1, 5, 11, 55
- Factors of 52 - The factors of 52 are 1, 2, 4, 13, 26, 52
- Factors of 99 - The factors of 99 are 1, 3, 9, 11, 33, 99
- Factors of 13 - The factors of 13 are 1, 13
- Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63
Factors of 5400 by Prime Factorization
- 5400 ÷ 2 = 2700
- 2700 ÷ 2 = 1350
- 1350 ÷ 2 = 675
Further dividing 675 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 675 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 5400 can be written as 23 × 33 × 52 where 2, 3, 5 are prime.
Factors of 5400 in Pairs
Pair factors of 5400 are the pairs of numbers that when multiplied give the product 5400. The factors of 5400 in pairs are:
- 1 × 5400 = (1, 5400)
- 2 × 2700 = (2, 2700)
- 3 × 1800 = (3, 1800)
- 4 × 1350 = (4, 1350)
- 5 × 1080 = (5, 1080)
- 6 × 900 = (6, 900)
- 8 × 675 = (8, 675)
- 9 × 600 = (9, 600)
- 10 × 540 = (10, 540)
- 12 × 450 = (12, 450)
- 15 × 360 = (15, 360)
- 18 × 300 = (18, 300)
- 20 × 270 = (20, 270)
- 24 × 225 = (24, 225)
- 25 × 216 = (25, 216)
- 27 × 200 = (27, 200)
- 30 × 180 = (30, 180)
- 36 × 150 = (36, 150)
- 40 × 135 = (40, 135)
- 45 × 120 = (45, 120)
- 50 × 108 = (50, 108)
- 54 × 100 = (54, 100)
- 60 × 90 = (60, 90)
- 72 × 75 = (72, 75)
Negative pair factors of 5400 are:
- -1 × -5400 = (-1, -5400)
- -2 × -2700 = (-2, -2700)
- -3 × -1800 = (-3, -1800)
- -4 × -1350 = (-4, -1350)
- -5 × -1080 = (-5, -1080)
- -6 × -900 = (-6, -900)
- -8 × -675 = (-8, -675)
- -9 × -600 = (-9, -600)
- -10 × -540 = (-10, -540)
- -12 × -450 = (-12, -450)
- -15 × -360 = (-15, -360)
- -18 × -300 = (-18, -300)
- -20 × -270 = (-20, -270)
- -24 × -225 = (-24, -225)
- -25 × -216 = (-25, -216)
- -27 × -200 = (-27, -200)
- -30 × -180 = (-30, -180)
- -36 × -150 = (-36, -150)
- -40 × -135 = (-40, -135)
- -45 × -120 = (-45, -120)
- -50 × -108 = (-50, -108)
- -54 × -100 = (-54, -100)
- -60 × -90 = (-60, -90)
- -72 × -75 = (-72, -75)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 5400 Solved Examples
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Example 1: How many factors are there for 5400?
Solution:
The factors of 5400 are too many, therefore if we can find the prime factorization of 5400, 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 5400 = 23 × 33 × 52
Therefore, the total number of factors are (3 + 1) × (3 + 1) × (2 + 1) = 4 × 4 × 3 = 48 -
Example 2: Find the LCM and Greatest Common Factor (GCF) of 5400 and 4275.
Solution:
The factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400 and factors of 4275 are 1, 3, 5, 9, 15, 19, 25, 45, 57, 75, 95, 171, 225, 285, 475, 855, 1425, 4275.
Therefore, the LCM of 5400 and 4275 is 102600 and Greatest Common Factor (GCF) of 5400 and 4275 is 225. -
Example 3: Find if 2, 72, 180, 300, 675, 1080, 2700 and 3920 are factors of 5400.
Solution:
When we divide 5400 by 3920 it leaves a remainder. Therefore, the number 3920 is not a factor of 5400. All numbers except 3920 are factors of 5400.
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Example 4: Find the product of all the prime factors of 5400.
Solution:
Since, the prime factors of 5400 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 5400
What are the Factors of 5400?
The factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400 and its negative factors are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -25, -27, -30, -36, -40, -45, -50, -54, -60, -72, -75, -90, -100, -108, -120, -135, -150, -180, -200, -216, -225, -270, -300, -360, -450, -540, -600, -675, -900, -1080, -1350, -1800, -2700, -5400.
What is the Sum of Factors of 5400?
Sum of all factors of 5400 = (23 + 1 - 1)/(2 - 1) × (33 + 1 - 1)/(3 - 1) × (52 + 1 - 1)/(5 - 1) = 18600
What Numbers are the Prime Factors of 5400?
The prime factors of 5400 are 2, 3, 5.
What is the Greatest Common Factor of 5400 and 3753?
The factors of 5400 and 3753 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400 and 1, 3, 9, 27, 139, 417, 1251, 3753 respectively.
Common factors of 5400 and 3753 are [1, 3, 9, 27].
Hence, the GCF of 5400 and 3753 is 27.
How Many Factors of 3121 are also common to the Factors of 5400?
Since, the factors of 5400 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 27, 30, 36, 40, 45, 50, 54, 60, 72, 75, 90, 100, 108, 120, 135, 150, 180, 200, 216, 225, 270, 300, 360, 450, 540, 600, 675, 900, 1080, 1350, 1800, 2700, 5400 and factors of 3121 are 1, 3121. Hence, 5400 and 3121 have only one common factor which is 1. Therefore, 5400 and 3121 are co-prime.
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