Factors of 51
Did you know that the number 51 is odd and is the product of two distinct prime numbers, 3 and 17? In this lesson, we will learn about the factors of 51, the prime factors of 51, and the factors of 51 in pairs with solved examples for a better understanding.
 Factors of 51: 1, 3, 17, and 51
 Prime Factorization of 51: 51 = 3 × 17
1.  What Are the Factors of 51? 
2.  Tips And Tricks 
3.  How to Calculate the Factors of 51? 
4.  Factors of 51 by Prime Factorization 
5.  Important Notes 
6.  Factors of 51 in Pairs 
7.  FAQs on Factors of 51 
What Are the Factors of 51?
The integers that divide 51 without leaving any remainder are called the factors of 51. For example, 17 divides 51 without leaving any remainder.
Hence, 17 is a factor of 51.
Interestingly, 3, which is the quotient of the above division, is also a factor of 51. Check whether you get 0 as the remainder when you divide 51 by 3 using long division.
Tips and Tricks:
 1 and the number itself are the factors of any number. Thus, every number has a minimum of two factors.
 Every number has a finite number of factors.
 Every factor of a number is less than or equal to the given number.
How to Calculate the Factors of 51?
To find the factors of 51, we have to find all the numbers which divide 51 and give the remainder as 0.
The divisors of all such divisions are the factors.
Hence, the factors of 51 are 1, 3, 17, and 51.
Explore factors using illustrations and interactive examples.
 Factors of 68  The factors of 68 are 1, 2, 4, 17, 34, and 68.
 Factors of 57  The factors of 57 are 1, 3, 19, and 57.
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
 Factors of 50  The factors of 50 are 1, 2, 5, 10, 25 and 50.
 Factors of 80  The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
 Factors of 17  The factors of 1 and 17.
Factors of 51 by Prime Factorization
The prime factorization of 51 is the product of prime numbers which results in 51.
Thus, the prime factorization of 51 is 51 = 3 × 17. From the prime factorization of 51, it is clear that 3 and 17 are the factors of 51.In fact, 3 and 17 are the prime factors of 51.
When 3 and 17 are the factors of 51, 3 × 17 = 51 is also a factor of 51.
Also, we know that 1 is a factor of every number. Thus, the factors of 51 by prime factorization are 1, 3, 17, and 51.
Important Notes:
 The prime numbers involved in the prime factorization of a number are the prime factors of the number.
 By multiplying the multiplicands of the prime factorization in different combinations, we can obtain the composite factors of the number.
 Fractions and decimals cannot be factors. Only integers (positive or negative) can be factors.
Factors of 51 in Pairs
The pair factors of 51 are obtained by writing 51 as a product of two numbers in all possible ways. In each case, both multiplicands are the factors of 51.
Product that Results in 51 
Pair Factors of 51 

1 × 51 
1, 51 
3 × 17 
3, 17 
The negative pair factors of 51 are (1, 51) and (3, 17).
Factors of 51 Solved Examples

Example 1: Can you try to solve the following riddle?
"I am a twodigit number. I lie between 10 and 20. I am a factor of 51. Who am I?"
Solution:
We already learned that the factors of 51 are 1, 3, 17, and 51.
The factor of 51 which is a twodigit number and lies between 10 and 20 is 17.
Hence, the answer to the riddle is 17.

Example 2: Mark was asked to find the prime factorization of 51 in his exam. He answered that the prime factorization of 51 is: 51 = 51 × 1.
But his teacher marked it wrong. Can we help him by giving the correct prime factorization?
Solution:
The above factorization of 51 is NOT a prime factorization as 51 and 1 are NOT prime numbers. Hence, we have to further express 3 and 17 as the product of prime numbers.
Hence, the prime factorization of 51 is 51 = 3 × 17.
FAQs on Factors of 51
What are all the factors of 51?
The factors of 51 are 1, 3, 17, and 51.
Why is 51 not a prime number?
51 has 4 factors which are 1, 3, 17, and 51.
Since 51 has more than 2 factors, it is not a prime number.
What are the common factors 51 and 50?
The factors of 51 are, 1, 3, 17, and 51. The factors of 50 are 1, 2, 5, 10, 25, and 50. The common factor of 51 and 50 is 1.
What are the factors of 51 and 85?
The factors of 51 are 1, 3, 17, and 51. The factors of 85 are 1, 5, 17, and 85.
What are the common factors of 51 and 93?
The factors of 51 are 1, 3, 17, and 51. The factors of 93 are 1, 3, 31, and 93. Thus, the common factors of 51 and 93 are 1 and 3.