Factors of 91

The numbers that divide 91 evenly are known as factors of 91. A factor of 91 is a number that divides the number without remainder. The factors of 91 are 1, 7, 13, and 91.

Negative factors of 91: -1, -7, -13, and -91.

Prime factors of 91: 7 and 13.

Prime factorization of 91: 7 × 13.

The sum of factors of 91: 1 + 7 + 13 + 91 = 112

Factors can be found using different methods. Mentioned below are some commonly used methods:

• Finding factors using multiplication
• Finding factors using division method
• Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 91. Identifying the numbers which are multiplied to get the number 91 is the multiplication method.

Step 1: Multiply 91 by 1, 91 × 1 = 91.

Step 2: Check for other numbers that give 91 after multiplying 7 × 13 = 91 Therefore, the positive factor pairs of 91 are: (1, 91), (7, 13).

All these factor pairs result in 91. For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 91 by 1, 91 ÷ 1 = 91.

Step 2: Continue dividing 91 by the numbers until the remainder becomes 0. 91 ÷ 1 = 91 91 ÷ 7 = 13 91 ÷ 13 = 7

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

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 91 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

91 ÷ 7 = 13

13 ÷ 13 = 1

The prime factors of 91 are 7 and 13. The prime factorization of 91 is: 7 × 13.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 91 is divided by 7 to get 13.

Step 2: Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 91 is: 7 × 13.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 91: (1, 91), (7, 13).
• Negative factor pairs of 91: (-1, -91), (-7, -13).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 91 are 1, 7, 13, and 91. Prime factors: The factors which are prime numbers. For example, 7 and 13 are prime factors of 91.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 91 are (1, 91) and (7, 13).

• Prime factorization: Breaking down a number into its basic prime number components. For example, the prime factorization of 91 is 7 × 13.

• Multiplication method: Finding factors by identifying number pairs that multiply to give the original number. For example, using multiplication to find factors of 91, we find 7 and 13.