Factors of 91

The factors of 91 are defined as the numbers which when divided to 91 should not leave any remainder. This means, 91 must be completely divisible by such a number that it does not leave any remainder. Some say 91 is a prime number, and some say 91 is a composite number. We will also get to know whether 91 is a prime number or not.

• The factors of a number are finite. It means, universally, that number will have a particular number of factors only.
• Composite numbers can only be factored in because they are made from the product of two or more numbers.
• Only integers and whole numbers can be factored in and will have factors.
• Every factor of a number is equal to less than the number itself.

The integer 91 can be divided only into two numbers – 1, 7, 13. It means, the product of 1, 7, 13 will result in the number 91.
Moreover, the number 91 will have the following factors: 1, 7, 13 and 91.
Therefore, the largest factor of 91 is 13, which is a prime number. The largest prime factor of 91 is 13. The number 91 can be written as: 91 = 7 x 13.
This means 91 is not a prime number. It is a composite number.

However, 91 will have the following categories of factors-
Positive factors: 1, 7, 13 and 91
Prime factors: 1, 7, 13
Negative factors: -7, -13
Prime factorization of 91 = 7 x 13

How to find the factors of 91?

The factors of 91 can be found by two methods –Long-division method and Prime factorization method.

Prime factorization method to find factors of 91

The prime factorization method is the most common method to find the factors of every number. Prime factorization also has another form, the prime factor tree method, which is a visual method to represent factors of every number. It helps in determining various prime factors of the number of our choice. A factor tree is not unique for a given number. Instead of expressing 91 as 7 x 13, we can represent 91 as 1 x 91.

We need to divide 91, from the smallest number to the largest number so that it completely divides the number-

• With the help of divisibility rules, we need to find out the smallest factor of the given number. Here, we have 91, which is an odd number. It is not divisible by 2. In other words, we need to look for another number greater than 2 that can divide 91 completely.
• We can also see, it is indivisible by 3. Therefore, we need to look for another prime number greater than 3.
• 5 also does not divide the number as 91 ends with 1; neither 0 nor 5.
• The other prime number is 7. We see 7 divides the number completely and leaves no remainder. Therefore, 7 is the first prime factor of 91.
• We need to look for other numbers that divide 91 completely. 91 ÷ 7 = 13, which is another prime number. 13 ÷ 13 = 1. Here, we get remainder 1. After this, our process is completed, and we get factors of 91.

Prime factorization of 91 using the prime factorization method is 7 x 13.

Example 1: What are the common factors of 91 and 92?

Solution: The factors of 91 are 1, 7, and 13.
The factors of 92 are 1, 2, 4, 23, 46, and 92.
Thus, the common factors of 91 and 92 are 1 only.