Is 91 a prime number?

Some may consider 91 a prime number at first glance, but it is actually a composite number. This means it holds more factors than just one and itself.

Let us see why it is composite:

1 = smallest divisor of any number

7 = prime number that divides 91 evenly

13 = another prime number that is a factor of 91

91 = itself the divisor.

As you can see, 91 contains four factors, making it a composite number.

91 is factored as 7×13. The prime number is only divisible by 1 and itself, where 91 has additional factors. 

Listed below are a few methods to find out whether a particular number is prime or composite.

Let us apply the counting divisors method for 91 to understand what it is not a prime number.

Step 1: Start with 1, always divisible.

Step 2: check square root of 91 = 9.54.

91 ÷ 2 = 45, not a divisible

91 ÷ 3 = 30, not a divisible

91 ÷ 7 = 13, is divisible.

Step 3: Find the pairs: 91 ÷ 13 = 7

Divisors = 1, 7, 13, 91

Total = 4 divisors

Hence, 91 has more than two divisors, it is not prime.
 

Let’s check with divisibility method, 91 is prime or not.

Step 1: Check divisibility by small prime numbers: 2, 3, 5.

2 =  odd, not divisible by 2.

3 = sum of digits 9+1=10 is not divisible by 3.

5 = last digit is not 0 or 5, so can not be divisible.

Step 2: Check divisibility by: 7

Trick is double the last digit and subtract from the rest

9-(2×1)=7,  

Then, the number 7 is divisible by 7, so 91 is divisible by 7.

Step 3: Calculate the other factors: 91 ÷ 7 =13

91= 7 ✕ 13

Hence, proved 91 is not prime. 

List the prime number chart up to 100.

The prime numbers up to 100 is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 89, 97. By keeping a note of the chart , we can easily find out, if a number is prime or not.

Prime factorization is only applicable to non-prime numbers/composite numbers. Since 91 has more than two factors 1, 7, 13, 91 it has possibility to factored into smaller prime numbers.
 

• Prime Number: A number which has only two divisors, that to be 1 and the other is the number itself.

• Composite Number: In mathematics, composite numbers are numbers that should have more than two factors, which is 1 and itself.

• Prime Factorization: In simple terms, prime factorization is a process of writing all numbers as a product of prime.