Factors of 407
Factors of 407 are numbers that, when multiplied in pairs give the product as 407. There are overall 4 factors of 407 among which 407 is the biggest factor and its positive factors are 1, 11, 37, 407. The sum of all factors of 407 is 456 and its factors in Pairs are (1, 407), (11, 37).
 All Factors of 407: 1, 11, 37 and 407
 Negative Factors of 407: 1, 11, 37 and 407
 Prime Factors of 407: 11, 37
 Prime Factorization of 407: 11^{1} × 37^{1}
 Sum of Factors of 407: 456
1.  What Are the Factors of 407? 
2.  Factors of 407 by Prime Factorization 
3.  Factors of 407 in Pairs 
4.  FAQs on Factors of 407 
What are Factors of 407?
Factors of 407 are pairs of those numbers whose products result in 407. These factors are either prime numbers or composite numbers.
How to Find the Factors of 407?
To find the factors of 407, we will have to find the list of numbers that would divide 407 without leaving any remainder.
 407/37 = 11; therefore, 37 is a factor of 407 and 11 is also a factor of 407.
 407/407 = 1; therefore, 407 is a factor of 407 and 1 is also a factor of 407.
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Factors of 407 by Prime Factorization
 407 ÷ 11 = 37
Further dividing 37 by 11 gives a nonzero remainder. So we stop the process and continue dividing the number 37 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 407 can be written as 11^{1} × 37^{1} where 11, 37 are prime.
Factors of 407 in Pairs
Pair factors of 407 are the pairs of numbers that when multiplied give the product 407. The factors of 407 in pairs are:
 1 × 407 = (1, 407)
 11 × 37 = (11, 37)
Negative pair factors of 407 are:
 1 × 407 = (1, 407)
 11 × 37 = (11, 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 407 Solved Examples

Example 1: How many factors are there for 407?
Solution:
The factors of 407 are 1, 11, 37, 407. Therefore, 407 has 4 factors.

Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 407 and 189.
Solution:
The factors of 407 are 1, 11, 37, 407 and factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189.
Therefore, the Lowest Common Multiple (LCM) of 407 and 189 is 76923 and Highest Common Factor (HCF) of 407 and 189 is 1. 
Example 3: Find if 11, 12 and 407 are factors of 407.
Solution:
When we divide 407 by 12 it leaves a remainder. Therefore, the number 12 is not a factor of 407. All numbers except 12 are factors of 407.

Example 4: Find the product of all the prime factors of 407.
Solution:
Since, the prime factors of 407 are 11, 37. Therefore, the product of prime factors = 11 × 37 = 407.
FAQs on Factors of 407
What are the Factors of 407?
The factors of 407 are 1, 11, 37, 407 and its negative factors are 1, 11, 37, 407.
What is the Sum of all Factors of 407?
All the Factors of 407 are 1, 11, 37, 407 and therefore the sum of all these factors is 1 + 11 + 37 + 407 = 456
What are the Prime Factors of 407?
The prime factors of 407 are 11, 37.
What is the Greatest Common Factor of 407 and 375?
The factors of 407 are 1, 11, 37, 407 and the factors of 375 are 1, 3, 5, 15, 25, 75, 125, 375. 407 and 375 have only one common factor which is 1. This implies that 407 and 375 are coprime.
Hence, the Greatest Common Factor (GCF) of 407 and 375 is 1.
How Many Factors of 206 are also common to the Factors of 407?
Since, the factors of 407 are 1, 11, 37, 407 and factors of 206 are 1, 2, 103, 206. Hence, 407 and 206 have only one common factor which is 1. Therefore, 407 and 206 are coprime.
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