Factors of 3240
Factors of 3240 are the list of integers that we can split evenly into 3240. There are total 40 factors of 3240, of which 2, 3, 5 are its prime factors. The sum of all factors of 3240 is 10890.
- All Factors of 3240: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620 and 3240
- Prime Factors of 3240: 2, 3, 5
- Prime Factorization of 3240: 23 × 34 × 51
- Sum of Factors of 3240: 10890
1. | What Are the Factors of 3240? |
2. | Factors of 3240 by Prime Factorization |
3. | Factors of 3240 in Pairs |
4. | FAQs on Factors of 3240 |
What are Factors of 3240?
Factors of 3240 are pairs of those numbers whose products result in 3240. These factors are either prime numbers or composite numbers.
How to Find the Factors of 3240?
To find the factors of 3240, we will have to find the list of numbers that would divide 3240 without leaving any remainder.
- 3240/5 = 648; therefore, 5 is a factor of 3240 and 648 is also a factor of 3240.
- 3240/810 = 4; therefore, 810 is a factor of 3240 and 4 is also a factor of 3240.
☛ Also Check:
- Factors of 19 - The factors of 19 are 1, 19
- Factors of 12 - The factors of 12 are 1, 2, 3, 4, 6, 12
- Factors of 57 - The factors of 57 are 1, 3, 19, 57
- Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 65 - The factors of 65 are 1, 5, 13, 65
Factors of 3240 by Prime Factorization
- 3240 ÷ 2 = 1620
- 1620 ÷ 2 = 810
- 810 ÷ 2 = 405
Further dividing 405 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 405 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 3240 can be written as 23 × 34 × 51 where 2, 3, 5 are prime.
Factors of 3240 in Pairs
Pair factors of 3240 are the pairs of numbers that when multiplied give the product 3240. The factors of 3240 in pairs are:
- 1 × 3240 = (1, 3240)
- 2 × 1620 = (2, 1620)
- 3 × 1080 = (3, 1080)
- 4 × 810 = (4, 810)
- 5 × 648 = (5, 648)
- 6 × 540 = (6, 540)
- 8 × 405 = (8, 405)
- 9 × 360 = (9, 360)
- 10 × 324 = (10, 324)
- 12 × 270 = (12, 270)
- 15 × 216 = (15, 216)
- 18 × 180 = (18, 180)
- 20 × 162 = (20, 162)
- 24 × 135 = (24, 135)
- 27 × 120 = (27, 120)
- 30 × 108 = (30, 108)
- 36 × 90 = (36, 90)
- 40 × 81 = (40, 81)
- 45 × 72 = (45, 72)
- 54 × 60 = (54, 60)
Negative pair factors of 3240 are:
- -1 × -3240 = (-1, -3240)
- -2 × -1620 = (-2, -1620)
- -3 × -1080 = (-3, -1080)
- -4 × -810 = (-4, -810)
- -5 × -648 = (-5, -648)
- -6 × -540 = (-6, -540)
- -8 × -405 = (-8, -405)
- -9 × -360 = (-9, -360)
- -10 × -324 = (-10, -324)
- -12 × -270 = (-12, -270)
- -15 × -216 = (-15, -216)
- -18 × -180 = (-18, -180)
- -20 × -162 = (-20, -162)
- -24 × -135 = (-24, -135)
- -27 × -120 = (-27, -120)
- -30 × -108 = (-30, -108)
- -36 × -90 = (-36, -90)
- -40 × -81 = (-40, -81)
- -45 × -72 = (-45, -72)
- -54 × -60 = (-54, -60)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 3240 Solved Examples
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Example 1: How many factors are there for 3240?
Solution:
The factors of 3240 are too many, therefore if we can find the prime factorization of 3240, 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 3240 = 23 × 34 × 51
Therefore, the total number of factors are (3 + 1) × (4 + 1) × (1 + 1) = 4 × 5 × 2 = 40 -
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 3240 and 1093.
Solution:
The factors of 3240 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240 and factors of 1093 are 1, 1093.
Therefore, the Lowest Common Multiple (LCM) of 3240 and 1093 is 3541320 and Greatest Common Divisor (GCD) of 3240 and 1093 is 1. -
Example 3: Find if 2, 4, 6, 10, 108, 162, 1620 and 2173 are factors of 3240.
Solution:
When we divide 3240 by 2173 it leaves a remainder. Therefore, the number 2173 is not a factor of 3240. All numbers except 2173 are factors of 3240.
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Example 4: Find the product of all the prime factors of 3240.
Solution:
Since, the prime factors of 3240 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 3240
What are the Factors of 3240?
The factors of 3240 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240 and its negative factors are -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -27, -30, -36, -40, -45, -54, -60, -72, -81, -90, -108, -120, -135, -162, -180, -216, -270, -324, -360, -405, -540, -648, -810, -1080, -1620, -3240.
What is the Sum of all the Factors of 3240?
Sum of all factors of 3240 = (23 + 1 - 1)/(2 - 1) × (34 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) = 10890
What are the Pair Factors of 3240?
The pair factors of 3240 are (1, 3240), (2, 1620), (3, 1080), (4, 810), (5, 648), (6, 540), (8, 405), (9, 360), (10, 324), (12, 270), (15, 216), (18, 180), (20, 162), (24, 135), (27, 120), (30, 108), (36, 90), (40, 81), (45, 72), (54, 60).
What is the Greatest Common Factor of 3240 and 1746?
The factors of 3240 and 1746 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240 and 1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746 respectively.
Common factors of 3240 and 1746 are [1, 2, 3, 6, 9, 18].
Hence, the Greatest Common Factor of 3240 and 1746 is 18.
How Many Factors of 3240 are also Factors of 1358?
Since, the factors of 3240 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240 and the factors of 1358 are 1, 2, 7, 14, 97, 194, 679, 1358.
Hence, [1, 2] are the common factors of 3240 and 1358.
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