Is 169 a Prime Number?

Did you know 169 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 2 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.

• Divisors of 169: 1,13 and 169.

• Number of divisors: 3

We can see that number 169 has three 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 169 is divisible by how many numbers. If 169 is divisible by even one of the numbers, then it will not be a prime number. Let's check the divisibility with 2,3,5,7 and 13. 

• That is, any number ending in an even number is divisible by 2. And 169 ends with an odd number. Actually, 9 is not a multiple of 2, so it is an odd number. So that 169 will not be divisible by 2 and it is not a prime number.

• The sum of the digits of the number 169 is 16. Now, in order to be divisible by 3, the sum of the digits needs to be a multiple of 3. Since 16 is not a multiple of 3. Therefore, 169 is not divisible by 3.

• It does not end in 0 or 5. To be divisible by 5 a number should end in 0 or 5. So, 169 cannot be divided by 5.

• We know how to see whether 169 is divisible by 7. Let's simply glance at the last digit, which is 9. We have doubled that 9 to get 18, then subtract the other digit, which is 16. So, we do 18 – 16 = 2. Since 2 is not a multiple of 7, it means that 169 is not divisible by 7.

• We know that for a number to be divisible by 13, we have to multiple 4 to the last digit of the number, here it is 9 and 4 times 9 is 36. We have to add 36 to the other digits, 36+16=52. We get 52. 52 is divisible by 13. Hence, 169 is divisible by 13.

We see that 169 is exactly divisible by one of the above numbers. Hence, 169 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 169 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 factors of 169 are 13 and 13. Since there are more than two factors for 169, we can not call 169 a prime number.
 

• Co-prime Numbers: These numbers have a GCF of 1. 

• Composite number: If the number of factors for the given number is above 2, then that number is a composite number.

• Multiple:The product we get while multiplying a number with another number.Example:- 10×2=20, 10×3=30. Here, 20 and 30 are multiples of 9.

• Square of a number: The product we get while a number is multiplied by itself. For example, 2 ² = 4; 3 ³ = 9; 4 × 4 = 16. That may be represented as 2², 3², 4².