101- A PRIME NUMBER? – MINDSPARK

IS 101 A PRIME NUMBER?

The answer to this question is – Yes, 101 is a prime number. Now, before we understand how 101 is a prime number, we should know what a prime number is. Prime numbers are simply numbers that only have two factors which are 1 and the number itself. They are not divisible by any other number. Some examples of prime numbers are 2, 3, 5, 7, 11, 13 and so on. The numbers that are not prime are called composite numbers. They have more than two factors. Examples of composite numbers are 4, 6, 8, 9, 10, 12, and so on. 

WHAT ARE THE FACTORS OF 101?

The factors of 101 are 1 and 101 themselves. This makes it a prime number. We cannot get 101 by multiplying any two other numbers. 

HOW TO FIND A PRIME NUMBER?

We can follow the given steps to check whether a number is a prime number or not:

Step 1: Check whether the number is divisible by 2. If it does not have 0, 2, 4, 6, or 8 at ones place then it is not divisible by 2.

Step 2: Check if the sum of the digits is divisible by 3 or not.

Step 3: Check if it is divisible by 5. It is only possible if it has 0 or 5 at ones place.

Step 4: Calculate the square root to check if it is a perfect square.

Step 5: Check for the divisibility with numbers less than 10.

HOW IS 101 A PRIME NUMBER?

We can follow the above-mentioned steps to check for the same.

Step 1: 101 is not divisible by 2 as it ends with 1.

Step 2: The sum of 1 + 0 + 1 = 2 which is not divisible by 3.

Step 3: The number doesn’t end in 0 or 5 so it is not divisible by 5.

Step 4: The square root is 10.04.

Step 5: Now we will check the divisibility with numbers less than 10. 

Divisibility with 4: The last two digits are 01 which is not divisible by 4 so 101 is not a multiple of 4

Divisibility with 6: The number 101 is neither divisible by 2 nor 3 so it is also not divisible by 6

Divisibility by 7: Multiply the last digit by 2. We get 1 x 2 = 2. Now subtract the product from the remaining number we get 10 – 2 = 8. 8 is not a multiple of 7 so 101 is not a multiple of 7 either.

Divisibility of 8: The number formed by the last 3 digits is 101, which is not divisible by 8.

Divisibility by 9: The sum of the digits 1 + 0 + 1 = 2 is not a multiple of 9 so 101 is not divisible by 9.

Thus, 101 has only two factors which are 1 and 101 and is a prime number.