Is 46 a Prime Number?

Did you know 46 isn’t a prime number? But why? Let us look at the rules a number has to follow to be a prime number to be a prime number.

• It should have only 2 factors: 1 and itself.

• It should have just 2 divisors.

In the rules which satisfy the two above, every number that comes next is of a prime number.

We could find that a number is prime if it has 2 factors only, 1 and the number itself. It means that a number, not satisfying these conditions, cannot be a prime number. However, there are pretty simple methods to determine whether a number is prime or not:

• Count Divisor Method

• Divisibility Test

• Prime Number Table

• Prime Factorization

Let's see how each of these tests helps us in finding prime numbers.
 

The name implies: We’re counting how many divisors a given number has, and then saying that number is prime. It is easy to learn. With that said, let’s see what steps are there in this method.

• Factors of 46: 1,2,23 and 46.

• Number of Factors: 4 

We can see that number 46 has four divisors. And we see that it doesn’t fulfill the criteria needed for a prime number. So it is not a prime number.
 

Let's check 46 is divisible by how many numbers. If 46 is divisible by even one of the numbers, then it will not be a prime number. Let's check the divisibility with 2,3,5 and 7. 

• That is, any number ending in an even number is divisible by 2. And 46 ends with an even number. Actually, 6 is a multiple of 2, so it is an even number. So that 46 will be divisible by 2 and it is not a prime number.

• The sum of the digits of the number 46 is 10. Now, in order to be divisible by 3, the sum of the digits needs to be a multiple of 3. Since 10 is not a multiple of 3. Therefore, 46 is not divisible by 3.

• 46 does not end in 0 or 5. To be divisible by 5 a number should end in 0 or 5. So, 46 cannot be divided by 5.

• We know how to see whether 46 is divisible by 7. Let's simply glance at the last digit, which is 6. We have doubled that 6 to get 12, then subtract the other digit, which is 4. So, we do 12 – 4 = 8. Since 8 is not a multiple of 7, it means that 46 is not divisible by 7.

We see that 46 is exactly divisible by one of the above numbers (divisible by 2). Hence, 46 is not a prime number.
 

Here, we will be using a chart that will contain all the prime numbers between 1 and 100. If the given number appears in the list, it is not a prime number. 
 

We can see that 46 does not appear here. So, it is not a prime number.
 

This method is used to break huge numbers into smaller numbers and find the prime factors of the given number.

We know the prime factorization of 46 is 2×23. Since there are more than two factors for 56, we can not call 56 a prime number.
 

• Test of divisibility: Test for the number to see how many numbers it is divisible by.. For example, 10. This unfortunately does not pass the divisibility test as it is divisible by 1, 2, 5 and 10.

• Composite number: A number is called a composite number if the number is greater than 1, and it has more than two factors. In the case of, example 16 is factorized as 2×8, so it is a composite number.

• Prime factors: Prime factors are prime numbers, multiplied to give you a bigger number. Suppose 18 is an example; it has prime factors of 2 and 3. 

• Prime Number Chart: Prime numbers form a list of course, often used to tell whether a number is prime, quickly checking if it appears in the list.