How to Determine if 91 is Prime: Method & Example
Prime numbers are the numbers that have only two factors, the number itself and 1.
To check if a number is prime or not we have to factorize it. So let us study whether 91 is a prime or composite number or why is 91, not a prime number? After factorizing 91, we get 4 factors. 91 has more than 2 factors i.e 1, 7,13, and 91 so 91 is not a prime number. In this article we will be studying what are prime numbers, how to determine a number, is prime or not, and is 91 a prime number?
What is a Composite Number?
Numbers containing more than two elements are called composite numbers. The number of components that a number has can be used to classify it. A prime number is one that contains just two factors: one and the number itself. Most numbers, however, include more than two elements and are referred to as composite numbers. We'll look at the distinction between prime and composite numbers, as well as the lowest composite number and odd composite numbers, on this page. The last one is intriguing because, unlike 2, which is the only even prime number, there exist multiple odd composite numbers.
What is the Prime Number?
A prime number is an integer greater than one and can be divisible by only itself and one i.e it has only two factors. Zero, 1, and numbers less than 1 are not considered prime numbers.
A number having more than two factors is referred to as a composite number. The smallest prime number is 2 because it is divisible by itself and 1 only.
Steps to Check Prime Number
To check whether any number is a prime number or not first we have to take factors of that number. If it has only two factors that are the number itself and 1 then it is a prime number. The following are the steps to check whether the given number is prime or not.
To check whether the number is a prime number, first, divide the number by 2 if it is completely divisible by 2 it is not a prime number but if it is not divisible by 2, try with 3. Take the square root of a number and check the division test till the number is less than the square root. If it is not divisible by any number then it is a not prime number or else it is a prime number. So let us check if 91 is a prime or composite number?
Now let us follow this step for 91 and see if 91 is a prime number or not.
Properties of a Prime Number
A prime number is a positive integer with two components that are precisely the same. If p is a prime, then the only factors it can have are 1 and p. A composite number is one that does not follow this pattern and maybe factored into other positive integers. A positive number or integer that is not a product of any other two positive integers other than 1 and the number itself is another method of describing it.
It's worth noting that 1 is a non-prime number. It's a one-of-a-kind number.
List of prime numbers to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
91 a Prime Number or Not
To find whether 91 is prime or composite, first, check whether (9+1) is divisible by 2 if not check it by 3.
We have, 9+1 is 10 which is not divisible by 3, continue with the following steps.
Step 1: First take the square root of 91, 91−−\[\sqrt{}\] = 9.53
Step 2: Choose prime numbers less than 9 and see if any of the numbers divide 91 completely.
Step 3: we get that the number 7 divides 91 perfectly. So, 91 is divisible by 7 we get more than two factors other than 1 and 91 itself. Hence, we can say that 91 is not a prime number.
So, why 91 is not a prime number is because it has more than two factors that contradict the definition of prime numbers.
91 is a Prime or Composite Number
As we can see why is 91 not a prime number it is because it has more than two factors other than 1 and the number itself. It contradicts the definition of prime numbers. So 91 is a composite number because composite numbers have factors more than 2.
When we factorize 91 we get
91 ÷ 1 = 91
91 ÷ 7 = 13
91 ÷ 13 = 7
91 ÷ 91 = 1
Here we get four factors for 91 and they are 1, 13, 7, 91. As the total number of factors is more than two it satisfies the condition of a composite number. Hence 91 is a composite number.
What Kind of Number is 91 Then?
Now it is clear that 91 does not satisfy the conditions of prime numbers. It satisfies the conditions for composite numbers so 91 is a composite number.
Some other kinds of numbers in which 91 falls are as follows:
A natural number
A positive integer
An odd number
A rational number
A composite number
A whole number
Solved Examples
Example 1: Is 19 a Prime Number or not?
Solution:
We can check the number is prime or not in two ways.
Method 1:
The formula for the prime number is 6n + 1
Let us write the given number in the form of 6n + 1.
6(3) + 1 = 18 + 1 = 19
Method 2:
Check for the factors of 19
19 has only two factors 1 and 19.
Therefore, by both methods, we get 19 as a prime number.
Example 2: Is 53 is a prime number or not?
Solution:
Method 1:
To know the prime numbers greater than 40, the below formula can be used.
n2 + n + 41, where n = 0, 1, 2, ….., 39
Put n= 3
32 + 3 + 41 = 9 + 3 + 41 = 53
Method 2:
53 has only factors 1 and 53.
So, 53 is a prime number by both the methods.
FAQs on Is 91 a Prime Number? Detailed Analysis & Answer
1. What is the main difference between a prime number and a composite number?
The main difference lies in the number of factors each has. A prime number has exactly two factors: 1 and the number itself. For example, the number 13 is prime because it is only divisible by 1 and 13. A composite number, on the other hand, has more than two factors. For example, the number 91 is composite because its factors are 1, 7, 13, and 91.
2. How can you prove that 91 is not a prime number?
You can prove 91 is not a prime number by finding a factor other than 1 and 91. This is done using the trial division method, where you test for divisibility by prime numbers (2, 3, 5, 7, etc.). Since 91 is an odd number, it is not divisible by 2. The sum of its digits (9+1=10) is not divisible by 3. It doesn't end in 0 or 5. When you test for 7, you find that 91 ÷ 7 = 13. Because 91 is perfectly divisible by 7, it has more than two factors, which proves it is a composite number.
3. Why is the number 1 considered neither prime nor composite?
The number 1 is unique because it does not fit the definition of either prime or composite numbers. The rules are:
- A prime number must have exactly two distinct factors.
- A composite number must have more than two factors.
The number 1 has only one factor: itself. Since it fails to meet the specific criteria for being prime or composite, it is classified as a special case.
4. What is the prime factorization of 91?
The prime factorization of a number is the expression of that number as a product of its prime factors. For 91, we find the smallest prime number that divides it. After checking 2, 3, and 5, we find that 91 is divisible by 7. Dividing 91 by 7 gives us 13. Since both 7 and 13 are prime numbers, the process stops. Therefore, the prime factorization of 91 is 7 × 13.
5. Are all odd numbers prime? Explain with an example.
No, not all odd numbers are prime. This is a common misconception. While 2 is the only even prime number, many odd numbers are composite. A number being odd only means it is not divisible by 2. For a number to be prime, it must not have any factors other than 1 and itself. For example, 91 is an odd number, but it is composite because it is divisible by 7 and 13. Other examples include 9, 15, and 25.
6. What is the smallest prime number, and why is the number 2 unique among all primes?
The smallest prime number is 2. The number 2 is unique because it is the only even prime number. By definition, all other even numbers are divisible by 2, which means they have at least three factors (1, 2, and themselves). This automatically makes every other even number a composite number, leaving 2 as the only even number that fits the definition of prime.
7. What are all the factors of 91?
A factor is a number that divides another number completely, leaving no remainder. To find all the factors of 91, we can use its prime factorization, which is 7 × 13. The factors include 1, the prime factors themselves, and the product of the prime factors. Therefore, the complete list of factors for 91 is 1, 7, 13, and 91.
8. How are prime numbers important in real life?
Prime numbers are fundamental to modern computer security and cryptography. When you perform secure actions online, like logging into an account or making a purchase, your data is protected using encryption. These encryption methods, such as RSA, rely on the mathematical difficulty of factoring a very large number that is the product of two large prime numbers. This ensures that sensitive information remains secure and unreadable to unauthorized parties.
