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Factors

Factors of 31 | Prime Factorization of 31 | Factor Tree of 31

Written by Prerit Jain

Updated on: 17 Aug 2023

Contents

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Factors of 31 | Prime Factorization of 31 | Factor Tree of 31

Factors of 31 | Prime Factorization of 31 | Factor Tree of 31

Factors of 31:  The factors of a number can be termed as the numbers that are completely divisible by a particular number. Here, the number 31 is a prime number. So, it can only be divided by 1 or by itself. This means, 31 has only two factors, i.e., 31 and 1.

A number can have both positive and negative factors, and they also come in pairs. In this article, we will examine how to find the factors of 31, its prime factorization, and the factor tree.

What Are the Factors of 31?

The factors of 31 are the numbers that divide the number (31) evenly without leaving any remainder. The factors of a number can be both positive and negative. Hence, the number 31 has both positive and negative factors.

Factors of 31: 1 and 31
Negative Factors of 31: -1 and -31
Prime Factorization of 31: 1 X 31 or 311
Pair Factors of 31:  1, 31
Prime Factors of 31: 31
Sum of Factors of 31: 1+ 31 = 32
Sum of Prime Factors of 31: 31
Factors of 31

 

What Are the Factors of 31 in Pairs?

The pair factor of 31 is a combination of two numbers, which when multiplied together gives the product of the original number (31). These pair factors are also written in positive and negative pairs as shown in the table below:

Positive Pair Factors of 31

The positive pair factors of 31 are (1, 31)

Positive Pair Factors of 31

Negative Pair Factors of 31

The negative pair factors of 31 are (-1, -31)

Negative Pair Factors of 31

How To Find Factors of 31 Through Division Method?

To determine the factors of 31, we are using the division method. This method requires us to take the given number (31) and divide it by a sequence of natural numbers. The number that can divide 31 evenly, without leaving reminders are the factors of 31. 31 is a prime number so, it can be divided only by 2 factors. They are 1 and 31.
The following are the steps for finding factors of 31 using the division method:

31 ÷ 1 = 31
31 ÷ 31 = 1

Hence, the factors 31 are 1 and 31.

What Is the Prime Factorization of 31?

Check if the given number is a prime number. If the given number is a prime number, then it has only two factors. If the given number is a composite number, then it has more than two factors.

Here, our given number is 31. 31 is a prime number so it has only 2 factors and they are 1 and 31. So there is no need to employ the prime factorization method to know the factors of 31. A visual representation of the prime factorization of 31 is given below to present a clearer idea:

Prime Factorization of 31

What is the Factor Tree of 31?

Students can also use the factor tree to find the prime factors of 31. This method will place the number 31 at the top of the factor tree. Now, as part of the branches, we will write down any set of pair factors of the given number (31). Now, again, we will split the pair of factors into factors. This process will be continued until the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 31.

  • Step 1: Let’s place the number 31 at the top of the factor tree and write down 31 in pairs, that is, 1 and 31.
  • Step 2: Since they are both prime numbers, we can no longer separate them.
  • Step 3: So, we circle them both. The factor branches no further and ends there.

There is only one way to write the factor tree of 31. Below is an image representation of the factor tree of 31:

Factor tree of 31

Solved Examples on Factors of 31

Here are some solved examples of 31 factors:

What is the sum of all the factors of 31?
1 and 31 are the factors of 31
1 + 31 = 32
Hence, 32 is the sum of all factors of 31.

What are the factors and prime factors of 31?
The factors of 31 are: 1 and 31.
The prime factor of 31 is 31.

What’s the highest common factor between 93 and 31?
The factors of 93 are 1, 3, 31, and 93.
Factors of 31 are 1 and 31.
Hence, from the above, the common factors of 93 and 31 are 1 and 31.
The highest common factor between 93 and 31 is 31.

What’s the highest common factor between 37 and 31?
The factors of 37 are 1 and 37.
The factors of 31 are 1 and 31.
Hence, from the above, the common factor of 37 and 31 is 1.
The highest and only common factor between 37 and 31 is 1.

Is 62 a factor of 31?
No, 62 is not a factor of 31.
62 ÷ 31 = 2.

What are the factors of -31?
The factors of -31 are -1 and -31.

What are all the factors of 31?
The factors of 31 are 1 and 31.

What are the factors of 31 that are composite?
Any number which has more than 2 factors is known as a composite number. But 31 is a prime number so it has no composite factors.
The factors of 31 are 1 and 31.

How many 31 factors are odd?
Factors of 31 have two odd numbers.
The factors of 31 are 1 and 31.

How many pair factors are there in 31?
A total of 1 pairs are there in factors of 31.

What is the largest factor of 31?
The largest factor of 31 is 31.
The second largest factor of 31 is 1.

FAQs on Factors of 31

List all the factors of 31 
1 and 31 are the 31 factors.

What are the factors of 31 in pairs?
(1, 31) is the only pair factor of 31.

What are the positive factors for 31?
1 and 31 are the positive factors for 31.

Is 62 divisible by 31?
Yes, 62 is divisible by 31.
62 ÷ 31 = 2

List the negative factors of 31.
The negative factors of 31 are -1 and -31.

Now that you have all the necessary information regarding the factors of 31, we hope this blog has been useful for you and easy to understand as well.

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Prerit Jain

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