Factors of 814
Factors of 814 are the list of integers that can be evenly divided into 814. There are 8 factors of 814, which are 1, 2, 11, 22, 37, 74, 407, 814. Here, 814 is the biggest factor. The Pair Factors of 814 are (1, 814), (2, 407), (11, 74), (22, 37) and its Prime Factors are 2 × 11 × 37.
 All Factors of 814: 1, 2, 11, 22, 37, 74, 407 and 814
 Negative Factors of 814: 1, 2, 11, 22, 37, 74, 407 and 814
 Prime Factors of 814: 2, 11, 37
 Prime Factorization of 814: 2^{1} × 11^{1} × 37^{1}
 Sum of Factors of 814: 1368
1.  What Are the Factors of 814? 
2.  Factors of 814 by Prime Factorization 
3.  Factors of 814 in Pairs 
4.  FAQs on Factors of 814 
What are Factors of 814?
Factors of 814 are pairs of those numbers whose products result in 814. These factors are either prime numbers or composite numbers.
How to Find the Factors of 814?
To find the factors of 814, we will have to find the list of numbers that would divide 814 without leaving any remainder.
 814/11 = 74; therefore, 11 is a factor of 814 and 74 is also a factor of 814.
 814/22 = 37; therefore, 22 is a factor of 814 and 37 is also a factor of 814.
☛ Also Check:
 Factors of 78  The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
 Factors of 27  The factors of 27 are 1, 3, 9, 27
 Factors of 16  The factors of 16 are 1, 2, 4, 8, 16
 Factors of 34  The factors of 34 are 1, 2, 17, 34
 Factors of 72  The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 814 by Prime Factorization
 814 ÷ 2 = 407
Further dividing 407 by 2 gives a nonzero remainder. So we stop the process and continue dividing the number 407 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 814 can be written as 2^{1} × 11^{1} × 37^{1} where 2, 11, 37 are prime.
Factors of 814 in Pairs
Pair factors of 814 are the pairs of numbers that when multiplied give the product 814. The factors of 814 in pairs are:
 1 × 814 = (1, 814)
 2 × 407 = (2, 407)
 11 × 74 = (11, 74)
 22 × 37 = (22, 37)
Negative pair factors of 814 are:
 1 × 814 = (1, 814)
 2 × 407 = (2, 407)
 11 × 74 = (11, 74)
 22 × 37 = (22, 37)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 814 Solved Examples

Example 1: How many factors are there for 814?
Solution:
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814. Therefore, 814 has 8 factors.

Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 814 and 759.
Solution:
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814 and factors of 759 are 1, 3, 11, 23, 33, 69, 253, 759.
Therefore, the Lowest Common Multiple (LCM) of 814 and 759 is 56166 and Greatest Common Divisor (GCD) of 814 and 759 is 11. 
Example 3: Find if 2, 11, 22, 407 and 481 are factors of 814.
Solution:
When we divide 814 by 481 it leaves a remainder. Therefore, the number 481 is not a factor of 814. All numbers except 481 are factors of 814.

Example 4: Find the product of all the prime factors of 814.
Solution:
Since, the prime factors of 814 are 2, 11, 37. Therefore, the product of prime factors = 2 × 11 × 37 = 814.
FAQs on Factors of 814
What are the Factors of 814?
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814 and its negative factors are 1, 2, 11, 22, 37, 74, 407, 814.
What is the Sum of all the Factors of 814?
Sum of all factors of 814 = (2^{1 + 1}  1)/(2  1) × (11^{1 + 1}  1)/(11  1) × (37^{1 + 1}  1)/(37  1) = 1368
What are Pair Factors of 814?
The pair factors of 814 are (1, 814), (2, 407), (11, 74), (22, 37).
What is the Greatest Common Factor of 814 and 111?
The factors of 814 and 111 are 1, 2, 11, 22, 37, 74, 407, 814 and 1, 3, 37, 111 respectively.
Common factors of 814 and 111 are [1, 37].
Hence, the Greatest Common Factor (GCF) of 814 and 111 is 37.
How Many Factors of 814 are also Factors of 79?
Since, the factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814 and factors of 79 are 1, 79. Hence, 814 and 79 have only one common factor which is 1. Therefore, 814 and 79 are coprime.
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