Factors of 2700
Factors of 2700 are integers that can be divided evenly into 2700. There are overall 36 factors of 2700 among which 2700 is the biggest factor and 2, 3, 5 are its prime factors. The Prime Factorization of 2700 is 22 × 33 × 52.
- All Factors of 2700: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350 and 2700
- Prime Factors of 2700: 2, 3, 5
- Prime Factorization of 2700: 22 × 33 × 52
- Sum of Factors of 2700: 8680
1. | What Are the Factors of 2700? |
2. | Factors of 2700 by Prime Factorization |
3. | Factors of 2700 in Pairs |
4. | FAQs on Factors of 2700 |
What are Factors of 2700?
Factors of 2700 are pairs of those numbers whose products result in 2700. These factors are either prime numbers or composite numbers.
How to Find the Factors of 2700?
To find the factors of 2700, we will have to find the list of numbers that would divide 2700 without leaving any remainder.
- 2700/12 = 225; therefore, 12 is a factor of 2700 and 225 is also a factor of 2700.
- 2700/450 = 6; therefore, 450 is a factor of 2700 and 6 is also a factor of 2700.
☛ Also Check:
- Factors of 50 - The factors of 50 are 1, 2, 5, 10, 25, 50
- 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, 180
- Factors of 21 - The factors of 21 are 1, 3, 7, 21
- Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 10 - The factors of 10 are 1, 2, 5, 10
Factors of 2700 by Prime Factorization
- 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 2700 can be written as 22 × 33 × 52 where 2, 3, 5 are prime.
Factors of 2700 in Pairs
Pair factors of 2700 are the pairs of numbers that when multiplied give the product 2700. The factors of 2700 in pairs are:
- 1 × 2700 = (1, 2700)
- 2 × 1350 = (2, 1350)
- 3 × 900 = (3, 900)
- 4 × 675 = (4, 675)
- 5 × 540 = (5, 540)
- 6 × 450 = (6, 450)
- 9 × 300 = (9, 300)
- 10 × 270 = (10, 270)
- 12 × 225 = (12, 225)
- 15 × 180 = (15, 180)
- 18 × 150 = (18, 150)
- 20 × 135 = (20, 135)
- 25 × 108 = (25, 108)
- 27 × 100 = (27, 100)
- 30 × 90 = (30, 90)
- 36 × 75 = (36, 75)
- 45 × 60 = (45, 60)
- 50 × 54 = (50, 54)
Negative pair factors of 2700 are:
- -1 × -2700 = (-1, -2700)
- -2 × -1350 = (-2, -1350)
- -3 × -900 = (-3, -900)
- -4 × -675 = (-4, -675)
- -5 × -540 = (-5, -540)
- -6 × -450 = (-6, -450)
- -9 × -300 = (-9, -300)
- -10 × -270 = (-10, -270)
- -12 × -225 = (-12, -225)
- -15 × -180 = (-15, -180)
- -18 × -150 = (-18, -150)
- -20 × -135 = (-20, -135)
- -25 × -108 = (-25, -108)
- -27 × -100 = (-27, -100)
- -30 × -90 = (-30, -90)
- -36 × -75 = (-36, -75)
- -45 × -60 = (-45, -60)
- -50 × -54 = (-50, -54)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 2700 Solved Examples
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Example 1: How many factors are there for 2700?
Solution:
The factors of 2700 are too many, therefore if we can find the prime factorization of 2700, 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 2700 = 22 × 33 × 52
Therefore, the total number of factors are (2 + 1) × (3 + 1) × (2 + 1) = 3 × 4 × 3 = 36 -
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 2700 and 1719.
Solution:
The factors of 2700 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700 and factors of 1719 are 1, 3, 9, 191, 573, 1719.
Therefore, the Least Common Multiple (LCM) of 2700 and 1719 is 515700 and Greatest Common Divisor (GCD) of 2700 and 1719 is 9. -
Example 3: Find if 1, 2, 20, 25, 60, 300, 540 and 1459 are factors of 2700.
Solution:
When we divide 2700 by 1459 it leaves a remainder. Therefore, the number 1459 is not a factor of 2700. All numbers except 1459 are factors of 2700.
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Example 4: Find the product of all the prime factors of 2700.
Solution:
Since, the prime factors of 2700 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 2700
What are the Factors of 2700?
The factors of 2700 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700 and its negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -27, -30, -36, -45, -50, -54, -60, -75, -90, -100, -108, -135, -150, -180, -225, -270, -300, -450, -540, -675, -900, -1350, -2700.
What is the Sum of the Factors of 2700?
Sum of all factors of 2700 = (22 + 1 - 1)/(2 - 1) × (33 + 1 - 1)/(3 - 1) × (52 + 1 - 1)/(5 - 1) = 8680
What numbers are the Pair Factors of 2700?
The pair factors of 2700 are (1, 2700), (2, 1350), (3, 900), (4, 675), (5, 540), (6, 450), (9, 300), (10, 270), (12, 225), (15, 180), (18, 150), (20, 135), (25, 108), (27, 100), (30, 90), (36, 75), (45, 60), (50, 54).
What is the Greatest Common Factor of 2700 and 1083?
The factors of 2700 and 1083 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700 and 1, 3, 19, 57, 361, 1083 respectively.
Common factors of 2700 and 1083 are [1, 3].
Hence, the Greatest Common Factor of 2700 and 1083 is 3.
How Many Factors of 2700 are also Factors of 943?
Since, the factors of 2700 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 90, 100, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 2700 and factors of 943 are 1, 23, 41, 943. Hence, 2700 and 943 have only one common factor which is 1. Therefore, 2700 and 943 are co-prime.
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