# Factors of 51

Definition of factors of 51: If a number completely divides 51 with the remainder zero, then that number is called a factor of 51.

By the above definition, we can say that the factors of 51 are the divisors of 51. In this section, we will learn about the factors of 51 and the prime factors of 51.

For more details: Basic concepts of factors

#### Highlights of Factors of 51

• 51=3×17 is the prime factorization of 51.
• The factors of 51 are 1, 3, 17 and 51.
• Prime factors of 51 are 3 and 17.
• Negative factors of 51 are –1, -3, -17 and –51.

#### What are the factors of 51?

Let us write the number 51 multiplicatively in all possible ways. We have:

 51 = 1×51 51 = 3×17

As we cannot express 51 multiplicatively in any other way, so we will stop right now. So the factors of 51 in pairs are given as follows:

 51 = a×b Factors in Pairs (a,b) 51 = 1×51 (1, 51) 51 = 3×17 (3, 17)

Thus the pair factors of 51 are (1, 51) and (3, 17). As all the numbers appearing in pair factors are the factors of 51, we conclude that

 The factors of 51 are: 1, 3, 17 and 51.

#### Number of factors of 51

From above we have calculated the factors of 51 which are 1, 3, 17 and 51. Thus the total number of factors of 51 is four.

#### Prime Factors of 51

Note that the factors of 51 are 1, 3, 17 and 51. Among those factors, we notice that only 3 and 17 are prime numbers as they do not have any proper divisors.

∴ the prime factor of 51 are 3 and 17.

Question: What are the factors of 51?

Video Solution: coming soon…

#### How to find factors of 51?

Now we will determine the factors of 51 by division method. In this method, we will find the numbers that can divide 51 with no remainder. See that

51/1=51 and the remainder is 0.

1 and 51 are factors of 51.

51/3=17 and the remainder is 0.

3 and 17 are factors of 51.

Note that no numbers other than the numbers in violet color can divide 51. So the numbers in violet color, that is, 1, 3, 17 and 51 are the complete list of factors of 51.