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Factors

Factors of 53 | Prime Factorization of 53 | Factor Tree of 53

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

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Factors of 53 | Prime Factorization of 53 | Factor Tree of 53

Factors of 53 | Prime Factorization of 53 | Factor Tree of 53

Factors of 53: Factors are a set of integers that can divide a given number evenly, without leaving a reminder.

The number 53 is a prime number. It has only two factors 1 and 53.


Factors can be written in both positive and negative formats. They can also occur as pairs. This means that multiplying the numbers within the pairs will yield a product that equals the given number.

In this article, we will find the factors of 53 using the division method, prime factorization, and factor tree method. Continue reading to learn more.

What Are the Factors of 53?


The factors of 53, like that of other numbers, divide 53 evenly without leaving any remainder. The factors can be positive and negative. Hence, the number 53 has both positive and negative factors.

Factors of 53: 1 and 53
Negative Factors of 53: -1 and -53
Prime Factorization of 53: 1 X 53 or 53X1
Pair Factors of 53: (1, 53)
Prime Factors of 53: 53
Sum of Factors of 53: 54
Sum of Prime Factors of 53: 53
Factors of 53

What Are the Factors of 53 in Pairs?

The pair factors of 53 are a combination of two numbers, which when multiplied by each other give 53 as a product. These pair factors are also written in positive and negative pairs as shown in the table below:

Positive Pair Factors of 53

The positive pair factor of 53 is (1, 53).

Positive Pair Factors of 53

Negative Pair Factors of 53

The negative pair factor of 53 is (-1, -53)

Negative Pair Factors of 53


How To Find Factors of 53 Through Division Method?

We are using the division method to determine the factors of 53. As per this approach, we will multiply 53 with a sequence of natural numbers. The numbers that divide 53 evenly are known as its factors. The following steps give a detailed account of how to find the factors of 53 using the division method:


• 53 ÷ 1 = 53
• 53 ÷ 53 = 1


We can see that 1 and 53 are the numbers that do not leave any remainder when divided by 53. So, they are the factors of 53.

What Is the Prime Factorization of 53?

Before we use the prime factorization method, we must check if the given number is a prime number. If the number is a prime number, then it has only two factors: 1 and 53. If not, then it has more than two factors.


53 is a prime number. It has only two factors. But let us employ the prime factorization method to present a better understanding of the concept.


The steps below help find the factors of 53 using the prime factorization method are given below:


Step 1: Divide 53 by the smallest prime number that can divide it. This number is 53.

53 ÷ 53 = 1

Step 2: Now we got 1 as the quotient. This brings us to the end of the factor tree.


Since 1 cannot be divided further, the prime factor of 53 is 53.

Image representation of the prime factorization of 53:

Prime Factorization of 53

What is the Factor Tree of 53?

The third method of finding the factors of 53 is the factor tree method. This method will place the number 53 on top of the factor tree. Now, as part of the branches, we will write down any set of pair factors of the given number (53). We will again split the pair of factors into factors. This process will go on until the branches become prime numbers.

Step 1: Let’s place the number 53 at the top of the factor tree. Since it is a prime number, the only two factors of 53 are 1 and 53.

Step 2: We cannot separate these numbers into branches anymore. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 53 or 53 X 1 = 53, which are 53 prime factors.

Below is an image representation of the factor tree of 53, choosing 1 and 53 as branches.

Factor tree of 53

Solved Examples of Factors of 53

Here are some solved examples of 53 factors:

What is the sum of all the factors of 53?
1 and 53 are the 53 factors.
1 + 53 = 54
Hence, 54 is the sum of all 53 factors.

What are the factors and prime factors of 53?
The 53 factors are 1 and 53.
The 53 prime factors are 53 X 1 or 53 X 1.

What’s the highest common factor between 53 and 16?
The factors of 53 are 1 and 53.
Factors of 16 are 1, 2, 4, 8, and 16.
Hence, from the above, the highest and only common factor of 53 and 16 is 1.

What’s the highest common factor between 53 and 63?
The factors of 53 are 1 and 53.
Factors of 63 are 1, 3, 7, 9, 21 and 63.
Hence, from the above, the highest and only common factor of 53 and 63 is 1.

What are the factors of -53?
The factors of -53 are -1 and -53.

What are all the factors of 53?
The factors of 53 are 1 and 53.

What are the factors of 53 that are composite?
Any number which has more than 2 factors is known as a composite number.
But 53 is a prime number. It has no composite factors.

How many 53 factors are odd?
All factors of 53 are odd. They are 1 and 53.

What are the factors of 31 and 53?
Factors 31 are 1 and 31.
The factors of 53 are 1 and 53.

What are the common factors of 53 and 106?
To list out the common factors of 53 and 106, we need to find the factors of both 53 and 106.
Factors of 53: 1 and 53
Factors of 106: 1, 2, 53 and 106
From the above, the common factors of 53 and 106 are 1 and 53.

How many different factors are there for the number 53?
A total of 2 factors are there for the number 53 and they are 1 and 53.

How many pair factors are there in 53?
A total of 1 pair is there in factors of 53.

What is the largest factor of 53?
The largest factor of 53 is 53.
The second largest factor of 53 is 1.

FAQs on Factors of 53

List all the factors of 53
1 and 53 are the 53 factors.

What are the composite factors of 53?
Composite factors are those that have more than 2 factors other than 1 and itself.
53 is a prime number. So, it has no composite factors.

What are the factors of 53 in pairs?
(1, 53) is the 53-pair factor.

What are the positive factors for 53?
1 and 53 are the positive factors for 53.

Is 477 divisible by 53?
Yes, 477 is divisible by 53. It is a multiple of 53.
477 ÷ 53 = 9

We have now covered all the necessary information about the factors of 53. We hope that this blog was useful and simple to understand.

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Prerit Jain

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