1. Steps to find factors of 91 using Division Method

Example: Find factors of 91

  • Divide 91 by 1: 91 ÷ 1 : Remainder = 0
  • Divide 91 by 7: 91 ÷ 7 : Remainder = 0
  • Divide 91 by 13: 91 ÷ 13 : Remainder = 0
  • Divide 91 by 91: 91 ÷ 91 : Remainder = 0

Hence, Factors of 91 are 1, 7, 13, and 91

2. Steps to find factors of 91 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 91 using the division method, follow these steps:

  • Step 1. Start dividing 91 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 91, which is 7. Divide 91 by 7 to obtain the quotient (13).
    91 ÷ 7 = 13
  • Step 3. Repeat step 1 with the obtained quotient (13).
    13 ÷ 13 = 1

So, the prime factorization of 91 is, 91 = 7 x 13.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 91 as shown below:

So, the prime factorization of 91 is, 91 = 7 x 13.

3. Find factors of 91 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 91 would be the two numbers which, when multiplied, give 91 as the result.

The following table represents the calculation of factors of 91 in pairs:

Factor Pair Pair Factorization
1 and 91 1 x 91 = 91
7 and 13 7 x 13 = 91

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 91. They are called negative pair factors.

Hence, the negative pairs of 91 would be ( -1 , -91 ) , ( -7 , -13 ) .

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of factors

  • Every number is a factor of zero (0), since 91 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 7, 13, 91 are exact divisors of 91.
  • Factors of 91 are 1, 7, 13, 91. Each factor divides 91 without leaving a remainder.

Frequently Asked Questions

  • What are the prime factors of 91?

    The factors of 91 are 1, 7, 13, 91.
    Prime factors of 91 are 7, 13.

  • What is the sum of all factors of 91?

    The sum of all factors of 91 is 112.

  • What are the pair factors of 91?

    Pair factors of 91 are (1,91), (7,13).

  • What two numbers make 91?

    Two numbers that make 91 are 7 and 13.

  • What are multiples of 91?

    First five multiples of 91 are 182, 273, 364, 455.

  • Is 91 a perfect square?

    No 91 is not a perfect square.

  • Which is greatest factor of 91?

    The greatest factor of 91 is 13.

  • How do you factors of 91?

    Factors of 91 are 1, 7, 13, 91.

  • What are five multiples of 91?

    First five multiples of 91 are 182, 273, 364, 455, 546.

Examples of Factors

Can you help Rubel to find out the product of the even factors of 91?

Factors of 91 are 1, 7, 13, 91.
Even factors of 91 are 0.
Hence, product of even factors of 91 is; 0 = 0.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 91? Help her in writing all the factors.

Positive factors are 1, 7, 13, 91.
Negative factors are -1, -7, -13, -91.

How many factors are there for 91?

Factors of 91 are 1, 7, 13, 91.
So there are in total 4 factors.

Sammy is puzzled while calculating the prime factors of 91. Can you help him find them?

Factors of 91 are 1, 7, 13, 91.
Prime factors of 91 are 7, 13

Joey wants to write all the prime factors of 91 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 91 are 7, 13.
So in exponential form it can be written as 7 x 13.

What is prime factorization of 91?

Prime factorization of 91 is 7 x 13 = 7 x 13.

Can you help Rubel to find out the product of the even factors of 91?

Factors of 91 are 1, 7, 13, 91.
Even factors of 91 are 0.
Hence, product of even factors of 91 is; 0 = 0.