Factors of 91

What are the Factors of 91?  

The number whose product is 91 after multiplication is known as the factors of 91. For example, let us take the number 17. It can be written as (1,17) and (-1,-17). When these are multiplied, they give us the number 17. 

Ways to Find the Factors of 91 

The factorisation procedure is used to find the factors of the number 91.

Pair Factor

Prime Factorization

1×91

7×13

7×13

 


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

In the pair factorisation process, you are first required to consider the numbers 1 and 91 as factors and then keep looking for pairs of numbers which when multiplied gives us the number 91.

Pair Factors of 91 are -

To locate the pairs of numbers which when multiplied gives us 91, we have to follow this method

Positive Pair Factors

Negative Pair Factors

1× 91 (1,19)

-1×-19 (-1,-19)

7×13  (7,13)

-7×-13 (-7,-13)

The two negative numbers, when multiplied together, cancel out each other's negative sign and give us a positive 91.

Prime Factorization Method to Find Factors of 91 -

The below-mentioned steps must be followed to find the factors of the number 91.

Let us take the number to be calculated as 91.

Now let's find the two numbers which when multiplied gives us the product 91 as a result. For example, 7×13 gives us 91.

While looking for factors for the numbers 7 and 13, we will see that these two numbers are prime numbers and only have two factors each.

Like the factors of 7 being=1×7

and the factors of 13 being = 1×13.

These two numbers only have two factors, the number itself and the number 1. Therefore, these two numbers cannot be factored anymore.

The number 91 when factorises using this method gives us 1,13, 7and 91 itself.

The numbers which have been acquired after the factorisation then must be written down as 7 ×13 ×1

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

Finding Prime Factors Through Division Process

Since the number 91 is a composite number, it is bound to have prime factors. Now let's go ahead and see how this method is to be used to find out the prime factors.

The first step that should be followed is dividing the number 91, with its smallest possible factor that is 7.

91/7 =13

Further, when 13 is divided by 7, a fraction will be obtained. A fraction cannot be a number's factor. Therefore, now you must use the next available prime factor, 13.

13/13 =1

At the end of the repeated divisions, we acquire the number 1. Therefore, we must stop here, as the process cannot be continued further. Thus the factors obtained must be written down as 7×13, where both 7 and 13 as we know are prime numbers.

Did You Know?

Did you know that a cube which is somewhere around 0.4 feet tall has the volume of 91 cubic inches?

Many people assume the number 91 to be a prime number, but in reality, it is a composite number.

FAQ (Frequently Asked Questions)

1. How Does Factorisation Help Us in Our Day to Day Lives? 

Factoring is an extremely useful knowledge which can be applied in our daily lives too. This skill can be applied when something needs to be divided equally, exchange of money, calculating time, comparing the prices of different items and also in the travel sector. Let us say, for example, 6 people joined hands to work towards baking brownies. After the process, 24 brownies were produced. Should everyone receive an equal number of brownies or should someone receive more while the other received less? To calculate this, we know that 6 is one of the factors of the number 24. Therefore, each of these 6 people should receive 4 brownies per individual without having to cut the brownies further into even smaller bits.

To calculate time, let us say that the doctor has prescribed you pills which you are required to take every 3 times in a day. A day is made up of 24 hours. So if you have to take 3 pills in a day, you have to take 1 pill at a regular interval of 8 hours (3×8 =24) time can be further divided into quarters of an hour. Since an hour contains 60 minutes, it can be expressed in quarters as 4 ×15=60 or into two parts of 30 minutes each that is, 2×30=60.

2. Is 91 a Prime Number or a Composite Number?

Factorisation plays an important part in finding out if 91 is a prime number or not. 

We already know that 1,7,13 and 91 are the factors of the number 91. Since there are already 4 factors of the number 91, the conditions for being a prime number are not met. 

In order to check the validity of the number 91 as a prime number, we have to first find out if the sum of the two digits (1+9) can be divided by 3. Since the sum total of the two numbers (1+9) is 10 and cannot be divided by 3, the below-mentioned procedure is to be followed next: - 

  • First, find the square root of the number 91, which gives us the result 9.53.

  • Next, select a number from the given prime numbers, which is less than 9 and then check if any of these selected numbers are able to divide 91 equally.

  • For the last step, it is observed that the prime number 7 can divide 91. Thus, we understand that 91 can be divided by 7, apart from 1 and the number itself.

Therefore, 91 is not a prime number but can be called a composite number since the number 91 is divisible by numbers other than 1 and itself and has four factors. It meets the demands of a composite number.