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Factors of 91 | Prime Factorization of 91 | Factor Tree of 91

Written by Prerit Jain

Updated on: 15 Feb 2023

Factors of 91 | Prime Factorization of 91 | Factor Tree of 91

Factors of 91 | Prime Factorization of 91 | Factor Tree of 91

When two numbers are multiplied together to get the result of 91, they are called factors of 91. The factors of 91 can be written in either positive or negative form. In this article, you will learn about factors of 91 using the factor tree method, prime factorization method, and division method.

What are the Factors of 91?

The numbers that divide 91 without leaving any remainder are known as factors of 91. The factors of 91 can be represented in both positive and negative forms. Prime numbers and composite numbers are the two major classifications found in the factors of 91. Any number which contains more than two factors is called a composite number. A number that has two factors or less than two factors is called a prime number. Since 91 has more than two factors it is called a composite number. The factors of 91 are 1, 7, 13, and 91.

Factors of 91: 1, 7, 13, and 91.
Negative Factors of 91:-1, -7, -13, and -91.
Prime Factorization of 91: 7 X 13
Pair Factors of 91: (1, 91), (7, 13)
Prime Factors of 91: 7 and 13
Sum of Factors of 91: 112
Sum of Prime Factors of 91: 20

What are the Factors of 91 in Pairs?

The factors of 91 can be both positive and negative. The combination of two numbers is called a pair factor of 91. When we multiply the pair factors of 91, the result will always be 91 and we will always get the original product.

Positive Pair Factors of 91

The positive pair factors of (1, 91), (7, 13)

Positive Pair Factors of 91

Negative Pair Factors of 91

The negative pair factors of (-1, -91), (-7, -13)

Negative Pair Factors of 91

How To Find Factors of 91 Through Division Method?

Any numbers that divide 91 without leaving any remainder are known as factors of 91. Through the division method, we can find the factors of 91 by a dividing sequence of numbers. The steps are mentioned below for your clear understanding.

91 ÷ 1 = 91
91 ÷ 7 = 13
91 ÷ 13 = 7

Therefore, the factors of 91 are 1, 7, 13, and 91.

Prime Factorization of 91

In the prime factorization method, you have to check whether the number 91 is a composite number or a prime number. Here, 91 is a composite number because it contains more than two factors, as we mentioned above. For your better understanding, we outlined everything in detail.

Step 1: Divide the number 91 by the smallest prime number that can divide evenly. That number is 7.
91÷ 7 = 13
Step 2: We get 13 as the quotient. Now, divide 13 by the smallest prime number which is 13 itself.
13 ÷ 13 = 1
The final quotient is 1. Since it cannot be divided further, the prime factors of 91 are 7 x 13 x 1. We can also write it down as 7 and 13, as both of them are prime numbers.
The prime factorization for 91 can be represented below:

Prime Factorization of 91

We can see that 1, 7, 13, and 91 are the numbers that do not leave any remainder when divided by 91. Thus they are the factors of 91.

What is the Factor Tree of 91?

Students can also use the factor tree to find the 91 prime factors. Let’s take 91 at the top of the factor tree. Then split the factors into factors and write down the set of the pair factors. This process is continued until the pair of factors turn into prime numbers. Finally, by identifying all the prime numbers we will get a prime factor of 91. The detailed steps on how to do this are explained below:

Step 1: Let’s place the number 91 at the top and write down 91 in pairs, that is, 7 and 13.
Step 2:  The branches in the factor tree will now be all the prime numbers.
Circling all the branches,  1 X 7 x 13, which are the prime factors of 91.
There are many ways in which we can write the factor tree of 91. Below is an image representation of the factor tree of 91, choosing 7 and 13 as pair factors of 91.

Factor tree of 91

Solved Examples of Factors of 91

What are the factors of 91?
The factors of 91 are 1, 7, 13, and 91.

What are the prime factors of 91?
The prime factors of 91 are 7 and 13.

What are the positive and negative pair factors of 91?
The positive pair factors of 91 are (1, 91), (7, 13) and the negative pair factors are (-1, -91), (-7, -13).

What is the sum of the factors of 91?
The sum of the factors of 91 is 112.

Frequently Asked Questions

How many factors do 91 have?
The factors of 91 are 1, 7, 13, and 91.

Is 91 divisible by all its factors?
The factors of 91 are 1, 7, 13, and 91 and 91 is divisible by all its factors. A factor is a number that divides another number completely and evenly.

What’s the prime factorization of 91?
In the prime factorization method, you have to check whether the number 91 is a composite number or a prime number. Here, 91 is a composite number because it contains more than two factors, as we mentioned above. For your better understanding, we outlined everything in detail.
Step 1: Divide the number 91 by the smallest prime number that can divide evenly. That number is 7.
91÷ 7 = 13
Step 2: We get 13 as the quotient. Now, divide 13 by the smallest prime number which is 13 itself.
13 ÷ 13 = 1
The final quotient is 1. Since it cannot be divided further, the prime factors of 91 are 7 x 13 x 1. We can also write it down as 7 and 13, as both of them are prime numbers.

What is the divisible of 91?
The divisible of 91 are 1, 7, 13, and 91.

Is 91 a natural number?
Yes, 91 is a natural number.

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Prerit Jain

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