Factors of 1210
Factors of 1210 are the list of integers that can be evenly divided into 1210. There are 12 factors of 1210 of which 1210 itself is the biggest factor and its prime factors are 2, 5, 11 The Prime Factorization of 1210 is 21 × 51 × 112.
- All Factors of 1210: 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605 and 1210
- Prime Factors of 1210: 2, 5, 11
- Prime Factorization of 1210: 21 × 51 × 112
- Sum of Factors of 1210: 2394
1. | What Are the Factors of 1210? |
2. | Factors of 1210 by Prime Factorization |
3. | Factors of 1210 in Pairs |
4. | FAQs on Factors of 1210 |

What are Factors of 1210?
Factors of 1210 are pairs of those numbers whose products result in 1210. These factors are either prime numbers or composite numbers.
How to Find the Factors of 1210?
To find the factors of 1210, we will have to find the list of numbers that would divide 1210 without leaving any remainder.
- 1210/1 = 1210; therefore, 1 is a factor of 1210.
- 1210/22 = 55; therefore, 22 is a factor of 1210.
☛ Also Check:
- Factors of 91 - The factors of 91 are 1, 7, 13, 91
- Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- Factors of 31 - The factors of 31 are 1, 31
- Factors of 72 - The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 1210 by Prime Factorization
- 1210 ÷ 2 = 605
Further dividing 605 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 605 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 1210 can be written as 21 × 51 × 112 where 2, 5, 11 are prime.
Factors of 1210 in Pairs
Pair factors of 1210 are the pairs of numbers that when multiplied give the product 1210. The factors of 1210 in pairs are:
- 1 × 1210 = (1, 1210)
- 2 × 605 = (2, 605)
- 5 × 242 = (5, 242)
- 10 × 121 = (10, 121)
- 11 × 110 = (11, 110)
- 22 × 55 = (22, 55)
Negative pair factors of 1210 are:
- -1 × -1210 = (-1, -1210)
- -2 × -605 = (-2, -605)
- -5 × -242 = (-5, -242)
- -10 × -121 = (-10, -121)
- -11 × -110 = (-11, -110)
- -22 × -55 = (-22, -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 1210 Solved Examples
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Example 1: How many factors are there for 1210?
Solution:
The factors of 1210 are too many, therefore if we can find the prime factorization of 1210, 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 1210 = 21 × 51 × 112
Therefore, the total number of factors are (1 + 1) × (1 + 1) × (2 + 1) = 2 × 2 × 3 = 12 -
Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 1210 and 1022.
Solution:
The factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210 and factors of 1022 are 1, 2, 7, 14, 73, 146, 511, 1022.
Therefore, the Lowest Common Multiple (LCM) of 1210 and 1022 is 618310 and Highest Common Factor (HCF) of 1210 and 1022 is 2. -
Example 3: Find if 1, 2, 55, 121, 242, 425 and 1210 are factors of 1210.
Solution:
When we divide 1210 by 425 it leaves a remainder. Therefore, the number 425 is not a factor of 1210. All numbers except 425 are factors of 1210.
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Example 4: Find the product of all the prime factors of 1210.
Solution:
Since, the prime factors of 1210 are 2, 5, 11. Therefore, the product of prime factors = 2 × 5 × 11 = 110.
FAQs on Factors of 1210
What are the Factors of 1210?
The factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210 and its negative factors are -1, -2, -5, -10, -11, -22, -55, -110, -121, -242, -605, -1210.
What is the Sum of Factors of 1210?
Sum of all factors of 1210 = (21 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (112 + 1 - 1)/(11 - 1) = 2394
What are Prime Factors of 1210?
The prime factors of 1210 are 2, 5, 11.
What is the Greatest Common Factor of 1210 and 751?
The factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210 and the factors of 751 are 1, 751. 1210 and 751 have only one common factor which is 1. This implies that 1210 and 751 are co-prime.
Hence, the Greatest Common Factor (GCF) of 1210 and 751 is 1.
What are the Common Factors of 1210 and 306?
Since, the factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210 and the factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306.
Hence, [1, 2] are the common factors of 1210 and 306.
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