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Factors

# Factors of 51 | Prime Factorization of 51 | Factor Tree of 51

Written by Prerit Jain

Updated on: 12 Aug 2023

### Factors of 51 | Prime Factorization of 51 | Factor Tree of 51

Factors of 51: Factors are a set of integers that can divide a given number evenly.

The number 51 has 4 factors – 1, 3, 17 and 51.

All numbers have factors that are positive and negative. They can also be arranged in pairs. Multiplying numbers within the pair will give the original number as the product.

In this article, we will discuss three methods to find the factors of 50. We will be using division methods, prime factorization, and factor trees. Keep reading to learn more

## What Are the Factors of 51?

The factors of 51 are those numbers that divide 51 evenly, leaving no reminder in the end. These factors can be positive and negative.

### Pair factors of 51

Pair factors of a number are a set of 2 numbers, which when multiplied together will give 51 as the product. They are illustrated in the tables below:

### Positive Pair Factors of 51

Positive pair factors of 51: (1, 51) and (3, 17).

### Negative Pair Factors of 51

Negative pair factors of 51: (-1, -51) and (-3, -17).

### How To Find Factors of 51 Through Division Method?

We will use the division method to find the factors of 51. We will do this by multiplying 51 with a sequence of integers. The numbers that divide 51 evenly are its factors. The following steps illustrate the use of the division method in finding factors of 51:

• 51 ÷ 1 = 51
• 51 ÷ 3 = 17
• 51 ÷ 17 = 3
• 51 ÷ 51 = 1

Thus, we can observe that 1, 3, 17, and 51 are the numbers that do not leave any remainder when divided by 51. So, they are the factors of 51.

### What Is the Prime Factorization of 51?

We will now use the prime factorization method to determine the factors of 51. Before performing the method, we must check if the given number is prime or composite in nature. If 51 is a prime number, it has only two factors: 1 and 51. If not, it has over two factors.

51 is the composite number. So, it will have more than two factors. Hence, we can find the factors of 51 using the prime factorization method.

The steps below give a detailed account of how we can use prime factorization to find the factors of 51:

Step 1: Divide the number 51 with the smallest prime number that can divide it. This smallest prime number is 3.
51 ÷ 3 = 17

Step 2: Now, divide 17 (quotient) by the smallest prime number, which is 17 itself. This is because 17 is also a prime number.
17 ÷ 17 = 1

The quotient 1 cannot be divided further. So, the prime factors of 51 are 3 X 17.
Image representation of the prime factorization of 51:

### What is the Factor Tree of 51?

We will now make use of the factor tree method to find the factors of 51. By the rules of this method, we will first place 51 on top of the factor tree. We will choose any one of its pair factors, as branches of the tree. We will divide these branches until all branches contain prime numbers.

Step 1: Let’s place the number 51 on top of the factor tree. Let us write down 3 and 17 as part of its branches.

Step 2: We can observe that 3 and 17 are both prime numbers. The branches in the factor tree will now be all the prime numbers. We have approached the end of our factor tree.

Hence, 17 X 3 = 51 are prime factors of 51.

Below is an image representation of the factor tree of 51, choosing 3 and 17 as pair factors.

### Solved Examples of Factors of 51

Here are some solved examples of 51 factors:

What is the sum of all the factors of 51?
1, 3, 17, and 51 are the 51 factors.
1 + 3 + 17 + 51 = 72
Hence, 72 is the sum of all 51 factors.

What are the factors and prime factors of 51?
The factors of 51 are 1, 3, 17, and 51.
The prime factors of 51 are 17 X 3.

What’s the highest common factor between 60 and 51?
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Factors of 51 are 1, 3, 17 and 51.
Hence, from the above, the common factors of 60 and 51 are 1 and 3
The highest common factor between 60 and 51 is 3.

What’s the highest common factor between 75 and 51?
Factors of 51: 1, 3, 17 and 51.
Factors of 75: 1, 3, 5, 15, 25 and 75.
Hence, the common factors of 51 and 75 are 1 and 3.
The highest common factor between 51 and 75 is 3.

Is 3 a factor of 51?
Yes, 3 is a factor of 51.
As 51 ÷ 17 = 3.

What are the factors of -51?
The factors of -51 are -1, -3, -17 and -51.

What are the common factors of 68 and 51?
To find the common factors of both these numbers, we need to find the factors first.
Factors of 68: 1, 2, 4, 17, 34 and 68
Factors of 51: 1, 3, 17 and 51
Hence the common factor of 68 and 51 is 17.

What are all the factors of 51?
The factors of 51 are 1, 3, 17 and 51.

What are the factors of 51 that are composite?
Any number which has more than 2 factors is known as a composite number. The composite factor of 51 is only 51.

How many 51 factors are odd?
All of the factors of 51 are odd. They are 1, 3, 17 and 51.

What are the factors of 51 and 17?
The factors of 51 are 1, 3, 17 and 51.
The factors of 17 are 1 and 17.

What are the common factors of 51 and 102?
To list out the common factors of 51 and 102, we need to find the factors of both numbers.
Factors of 51: 1, 3, 17 and 51
Factors of 102: 1, 2, 3, 6, 17, 34, 51 and 102
From the above, the common factors of 51 and 102 are 1, 3, 17, 51.

How many different factors are there for the number 51?
A total of 4 factors are there for the number 51 and are 1, 3, 17 and 51.

How many pair factors are there in 51?
A total of 2 pairs are there in factors of 51.

What is the largest factor of 51?
The largest factor of 51 is 51.
The second largest factor of 51 is 17.

### FAQs on Factors of 51

List all the factors of 51
1, 3, 17, and 51 are the 51 factors.

What are the composite factors of 51?
The only composite factor of 51 is 51.
Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 51 in pairs?
(1, 51) and (3, 17) are the 51 factors of pairs.

What are the positive factors for 51?
1, 3, 17 and 51 are the positive factors for 51.

What are the first 10 multiples of 51?
The first 10 multiples of 51 are 51, 102, 153, 204, 255, 306, 357, 408, 459, 510

Now that you have all the necessary information regarding the factors of 51. We hope this blog has been useful and easy to understand.

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Prerit Jain

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