Factors of 2340
Factors of 2340 are numbers that, when multiplied in pairs give the product as 2340. There are overall 36 factors of 2340, of which 2, 3, 5, 13 are its prime factors. The sum of all factors of 2340 is 7644.
- All Factors of 2340: 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 180, 195, 234, 260, 390, 468, 585, 780, 1170 and 2340
- Prime Factors of 2340: 2, 3, 5, 13
- Prime Factorization of 2340: 22 × 32 × 51 × 131
- Sum of Factors of 2340: 7644
1. | What Are the Factors of 2340? |
2. | Factors of 2340 by Prime Factorization |
3. | Factors of 2340 in Pairs |
4. | FAQs on Factors of 2340 |
What are Factors of 2340?
Factors of 2340 are pairs of those numbers whose products result in 2340. These factors are either prime numbers or composite numbers.
How to Find the Factors of 2340?
To find the factors of 2340, we will have to find the list of numbers that would divide 2340 without leaving any remainder.
- 2340/1170 = 2; therefore, 1170 is a factor of 2340 and 2 is also a factor of 2340.
- 2340/5 = 468; therefore, 5 is a factor of 2340 and 468 is also a factor of 2340.
☛ Also Check:
- Factors of 121 - The factors of 121 are 1, 11, 121
- Factors of 7 - The factors of 7 are 1, 7
- Factors of 72 - The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 100 - The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
- Factors of 15 - The factors of 15 are 1, 3, 5, 15
Factors of 2340 by Prime Factorization
- 2340 ÷ 2 = 1170
- 1170 ÷ 2 = 585
Further dividing 585 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 585 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 2340 can be written as 22 × 32 × 51 × 131 where 2, 3, 5, 13 are prime.
Factors of 2340 in Pairs
Pair factors of 2340 are the pairs of numbers that when multiplied give the product 2340. The factors of 2340 in pairs are:
- 1 × 2340 = (1, 2340)
- 2 × 1170 = (2, 1170)
- 3 × 780 = (3, 780)
- 4 × 585 = (4, 585)
- 5 × 468 = (5, 468)
- 6 × 390 = (6, 390)
- 9 × 260 = (9, 260)
- 10 × 234 = (10, 234)
- 12 × 195 = (12, 195)
- 13 × 180 = (13, 180)
- 15 × 156 = (15, 156)
- 18 × 130 = (18, 130)
- 20 × 117 = (20, 117)
- 26 × 90 = (26, 90)
- 30 × 78 = (30, 78)
- 36 × 65 = (36, 65)
- 39 × 60 = (39, 60)
- 45 × 52 = (45, 52)
Negative pair factors of 2340 are:
- -1 × -2340 = (-1, -2340)
- -2 × -1170 = (-2, -1170)
- -3 × -780 = (-3, -780)
- -4 × -585 = (-4, -585)
- -5 × -468 = (-5, -468)
- -6 × -390 = (-6, -390)
- -9 × -260 = (-9, -260)
- -10 × -234 = (-10, -234)
- -12 × -195 = (-12, -195)
- -13 × -180 = (-13, -180)
- -15 × -156 = (-15, -156)
- -18 × -130 = (-18, -130)
- -20 × -117 = (-20, -117)
- -26 × -90 = (-26, -90)
- -30 × -78 = (-30, -78)
- -36 × -65 = (-36, -65)
- -39 × -60 = (-39, -60)
- -45 × -52 = (-45, -52)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 2340 Solved Examples
-
Example 1: How many factors are there for 2340?
Solution:
The factors of 2340 are too many, therefore if we can find the prime factorization of 2340, 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 2340 = 22 × 32 × 51 × 131
Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) × (1 + 1) = 3 × 3 × 2 × 2 = 36 -
Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 2340 and 1849.
Solution:
The factors of 2340 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 180, 195, 234, 260, 390, 468, 585, 780, 1170, 2340 and factors of 1849 are 1, 43, 1849.
Therefore, the Lowest Common Multiple (LCM) of 2340 and 1849 is 4326660 and Highest Common Factor (HCF) of 2340 and 1849 is 1. -
Example 3: Find if 12, 18, 78, 90, 156, 180, 468 and 2251 are factors of 2340.
Solution:
When we divide 2340 by 2251 it leaves a remainder. Therefore, the number 2251 is not a factor of 2340. All numbers except 2251 are factors of 2340.
-
Example 4: Find the product of all the prime factors of 2340.
Solution:
Since, the prime factors of 2340 are 2, 3, 5, 13. Therefore, the product of prime factors = 2 × 3 × 5 × 13 = 390.
FAQs on Factors of 2340
What are the Factors of 2340?
The factors of 2340 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 180, 195, 234, 260, 390, 468, 585, 780, 1170, 2340 and its negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -13, -15, -18, -20, -26, -30, -36, -39, -45, -52, -60, -65, -78, -90, -117, -130, -156, -180, -195, -234, -260, -390, -468, -585, -780, -1170, -2340.
What is the Sum of all Factors of 2340?
Sum of all factors of 2340 = (22 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (131 + 1 - 1)/(13 - 1) = 7644
What are the Pair Factors of 2340?
The pair factors of 2340 are (1, 2340), (2, 1170), (3, 780), (4, 585), (5, 468), (6, 390), (9, 260), (10, 234), (12, 195), (13, 180), (15, 156), (18, 130), (20, 117), (26, 90), (30, 78), (36, 65), (39, 60), (45, 52).
What is the Greatest Common Factor of 2340 and 465?
The factors of 2340 and 465 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 180, 195, 234, 260, 390, 468, 585, 780, 1170, 2340 and 1, 3, 5, 15, 31, 93, 155, 465 respectively.
Common factors of 2340 and 465 are [1, 3, 5, 15].
Hence, the Greatest Common Factor of 2340 and 465 is 15.
How Many Factors of 2340 are also common to the Factors of 101?
Since, the factors of 2340 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 18, 20, 26, 30, 36, 39, 45, 52, 60, 65, 78, 90, 117, 130, 156, 180, 195, 234, 260, 390, 468, 585, 780, 1170, 2340 and factors of 101 are 1, 101. Hence, 2340 and 101 have only one common factor which is 1. Therefore, 2340 and 101 are co-prime.
visual curriculum