What are the factors of 91?
Natural numbers that divide 91 without leaving any remainder are known as factors of 91. In other words, the numbers that are multiplied together in pairs, resulting in the number 91, are the factors of 91. The factors of 91 can be positive or negative, but the factors of 91 cannot be fractions or decimals. The factors of 91 are 1, 7, 13, and 91.
List of factors of 91
So the factors of 91 are 1, 7, 13, and 91.
Factors of 91 by Division Method
We can check whether a number is a factor of 91 by dividing 91 by that number and checking if the remainder is zero or not. If the remainder is zero, the number is a factor of 91.
- If we divide 91 by 1, we get the quotient and remainder as 91 and 0, respectively. So, 1 is the factor of 91.
- If we divide 91 by 7, we get the quotient and remainder as 13 and 0, respectively. So, 7 is the factor of 91.
- If we divide 91 by 13, we get the quotient and remainder as 7 and 0, respectively. So, 13 is the factor of 91.
- If we divide 91 by 91, we get the quotient and remainder as 1 and 0, respectively. So, 91 is the factor of 91.
[Note: If we divide 91 by 10, we get the quotient and remainder as 10 and 1, respectively. This means the remainder is not zero. So 10 is not a factor of 91.]
Prime Factorization of 91
When a number is expressed as a product of prime numbers then these prime numbers are known as prime factors of the original number. The process of writing this multiplication of prime factors is known as prime factorization.
Prime factorization of 91 can be represented using a factor tree as follows:
So, the prime factorization of 91 is 91 = 7 x 13 and the prime factors of 91 are 7 and 13.
Factor Pairs of 91
The factor pair of a number is the set of its two factors such that their product is equal to the original number.
We can write the factor pairs of 91 using the list of factors of 91, that is,
1 x 91 = 91
7 x 13 = 91
We can also write the factor pairs in ordered pairs: (1, 91), (7, 13).
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Solved Factors of 91 Examples
Example 1: Find the common factor of 90 and 91.
Solution:
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
Factors of 91 = 1, 7, 13 and 91.
Therefore, the common factor of 90 and 91 is 1.
Example 2: Find the greatest common factor of 65 and 91.
Solution:
Factors of 65 = 1, 5, 13 and 65
Factors of 91 = 1, 7, 13 and 91
The common factors of 65 and 91 are 1 and 13.
Therefore, the greatest common factor of 65 and 91 is 13.
Example 3: Find the least common prime factor of 91 and 133.
Solution:
Factors of 91 = 1, 7, 13 and 91
Factors of 133 = 1, 7, 19 and 133
The common factors of 91 and 133 are 1 and 7.
Therefore, the least common prime factor of 91 and 133 is 7.
Example 4: Andrew needs to draw a rectangular sketch of an area of 91 cm\(^2\) on paper. Find the possible dimensions of the rectangular sketch.
Solution :
The area of a rectangular sketch is calculated by multiplying its length and breadth, that is,
Area = length x breadth
91 = length x breadth [Substitute 91 for area]
So the factor pairs of 91 will be the possible dimensions, length and breadth, of the rectangular sketch.
Hence, the possible dimensions are :
Factors of 91 are natural numbers that divide 91 evenly.
The factors of 91 are 1, 7, 13 and 91.
So, the sum of the factors of 91 = 1 + 7 + 13 + 91 = 112
Yes, when we divide 91 by 13 we get 0 as the remainder and 7 as the quotient.
91 has factors other than 1 and itself. The factors of 91 other than 1 and itself are 7 and 13. So 91 is not a prime number.
The composite numbers are those numbers which have a factor other than 1 and itself. For example 18, 44, 55 and so on.