Factors of 2310
Factors of 2310 are the list of integers that can be evenly divided into 2310. There are overall 32 factors of 2310, of which 2, 3, 5, 7, 11 are its prime factors. The Prime Factorization of 2310 is 21 × 31 × 51 × 71 × 111.
- All Factors of 2310: 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155 and 2310
- Prime Factors of 2310: 2, 3, 5, 7, 11
- Prime Factorization of 2310: 21 × 31 × 51 × 71 × 111
- Sum of Factors of 2310: 6912
1. | What Are the Factors of 2310? |
2. | Factors of 2310 by Prime Factorization |
3. | Factors of 2310 in Pairs |
4. | FAQs on Factors of 2310 |
![Factors of 2310](https://static.qumath.in/static/website/old-cdn-static/factors/factors-of-2310.png)
What are Factors of 2310?
Factors of 2310 are pairs of those numbers whose products result in 2310. These factors are either prime numbers or composite numbers.
How to Find the Factors of 2310?
To find the factors of 2310, we will have to find the list of numbers that would divide 2310 without leaving any remainder.
- 2310/110 = 21; therefore, 110 is a factor of 2310 and 21 is also a factor of 2310.
- 2310/35 = 66; therefore, 35 is a factor of 2310 and 66 is also a factor of 2310.
☛ Also Check:
- Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 21 - The factors of 21 are 1, 3, 7, 21
- Factors of 41 - The factors of 41 are 1, 41
- Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 2310 by Prime Factorization
- 2310 ÷ 2 = 1155
Further dividing 1155 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 1155 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 2310 can be written as 21 × 31 × 51 × 71 × 111 where 2, 3, 5, 7, 11 are prime.
Factors of 2310 in Pairs
Pair factors of 2310 are the pairs of numbers that when multiplied give the product 2310. The factors of 2310 in pairs are:
- 1 × 2310 = (1, 2310)
- 2 × 1155 = (2, 1155)
- 3 × 770 = (3, 770)
- 5 × 462 = (5, 462)
- 6 × 385 = (6, 385)
- 7 × 330 = (7, 330)
- 10 × 231 = (10, 231)
- 11 × 210 = (11, 210)
- 14 × 165 = (14, 165)
- 15 × 154 = (15, 154)
- 21 × 110 = (21, 110)
- 22 × 105 = (22, 105)
- 30 × 77 = (30, 77)
- 33 × 70 = (33, 70)
- 35 × 66 = (35, 66)
- 42 × 55 = (42, 55)
Negative pair factors of 2310 are:
- -1 × -2310 = (-1, -2310)
- -2 × -1155 = (-2, -1155)
- -3 × -770 = (-3, -770)
- -5 × -462 = (-5, -462)
- -6 × -385 = (-6, -385)
- -7 × -330 = (-7, -330)
- -10 × -231 = (-10, -231)
- -11 × -210 = (-11, -210)
- -14 × -165 = (-14, -165)
- -15 × -154 = (-15, -154)
- -21 × -110 = (-21, -110)
- -22 × -105 = (-22, -105)
- -30 × -77 = (-30, -77)
- -33 × -70 = (-33, -70)
- -35 × -66 = (-35, -66)
- -42 × -55 = (-42, -55)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 2310 Solved Examples
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Example 1: How many factors are there for 2310?
Solution:
The factors of 2310 are too many, therefore if we can find the prime factorization of 2310, 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 2310 = 21 × 31 × 51 × 71 × 111
Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 × 2 = 32 -
Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 2310 and 1448.
Solution:
The factors of 2310 are 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310 and factors of 1448 are 1, 2, 4, 8, 181, 362, 724, 1448.
Therefore, the Least Common Multiple (LCM) of 2310 and 1448 is 1672440 and Highest Common Factor (HCF) of 2310 and 1448 is 2. -
Example 3: Find if 11, 14, 55, 77, 154, 462, 770 and 1974 are factors of 2310.
Solution:
When we divide 2310 by 1974 it leaves a remainder. Therefore, the number 1974 is not a factor of 2310. All numbers except 1974 are factors of 2310.
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Example 4: Find the product of all the prime factors of 2310.
Solution:
Since, the prime factors of 2310 are 2, 3, 5, 7, 11. Therefore, the product of prime factors = 2 × 3 × 5 × 7 × 11 = 2310.
FAQs on Factors of 2310
What are the Factors of 2310?
The factors of 2310 are 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310 and its negative factors are -1, -2, -3, -5, -6, -7, -10, -11, -14, -15, -21, -22, -30, -33, -35, -42, -55, -66, -70, -77, -105, -110, -154, -165, -210, -231, -330, -385, -462, -770, -1155, -2310.
What is the Sum of the Factors of 2310?
Sum of all factors of 2310 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) × (111 + 1 - 1)/(11 - 1) = 6912
What Numbers are the Prime Factors of 2310?
The prime factors of 2310 are 2, 3, 5, 7, 11.
What is the Greatest Common Factor of 2310 and 461?
The factors of 2310 are 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310 and the factors of 461 are 1, 461. 2310 and 461 have only one common factor which is 1. This implies that 2310 and 461 are co-prime.
Hence, the Greatest Common Factor (GCF) of 2310 and 461 is 1.
What are the Common Factors of 2310 and 1232?
Since, the factors of 2310 are 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310 and the factors of 1232 are 1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 44, 56, 77, 88, 112, 154, 176, 308, 616, 1232.
Hence, [1, 2, 7, 11, 14, 22, 77, 154] are the common factors of 2310 and 1232.
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