How to find out if a number is a prime number?

Math is best learnt through activities. Here’s a beautiful activity that helps you find out if a number is prime or composite. This activity works best for numbers between 2 to 100.

Activity to find out all Prime Numbers till 100

Start with a grid with numbers listed from 1 to 100. We cross out 1 because Prime numbers are defined for numbers greater than 1.

Step 1: We have crossed out 1. So we start with the next available number. That’s 2. Circle it. This is your first prime number.
Step 2: Now cross out all multiples of 2. Continue until you reach the end of the grid. So almost half the number up to 100 will get crossed out. These cannot be prime as they have 2 as their factor apart from 1 and themselves. So all multiples are composite numbers.
Step 3: Move to the next available number. That will be 3. Circe it. You’ve found another prime number!
Step 4: Cross out all multiples of 3. Continue until you reach the end of the grid. If a number is already crossed out, e.g. 6 just move on. The last number you’ll cross out will be 99.
Step 5: Move to the next available number. This will be 5. Circle it. You’ve found another prime number!
Step 6: Cross out all multiples of 5.
Step 7: Move to the next available number and circle it. Then cross out its multiples. Repeat step 7 till all numbers on the grid are either crossed or circled.

The numbers you circled are Prime Numbers. The numbers you crossed are composite numbers.

Another quick way to find if a number is a prime number or not

Is 97 a prime number?

We use divisibility rules to quickly find out if 97 is divisible by 2, 3, 5.

97 is an odd number - so not divisible by 2.
The digits of 97 add up to 16 which is not divisible by 3. So 97 is not divisible by 3.
Since the units place digit is not 0 or 5, 97 is not divisible by 5.
We can skip 4, 6, 8, 9, 10, 12 and 15 as any number divisible by these would have also been divisible by 2 or 3 or 5.

Now let’s check some of the subsequent numbers like 7 and 11. Using whichever technique including long division we see that 97 is not divisible by any of these numbers.

Also, observe that 11 x 9 = 99, a number greater than 97. That means we’ve gone past the square root of 97. This gives us an important clue. If you’ve gone past the square root of the given number without finding any factors, then you need not continue. You won't find any new factors.
The reason for this is for all subsequent numbers (larger than 11), the multiplicand will be smaller than 9. Since we’ve checked all numbers till 9 (in fact till 11 already), we know that no pair of factors is possible. Remember all factors pairs will have one number smaller than the square root and the other larger than the square root. (A factor pair is a set of two numbers which when multiplied give you the original number whose factors you’re identifying).

Thus 97 does not have any factors apart from 1 and 97. So, 97 is a prime number.