A main quantity is a quantity that’s divisible solely by 1 and itself. A quantity is divisible by one other quantity when the rest is zero.

For instance, 7 is a main quantity as a result of 7 is just divisible by 1 and seven. Which means that in the event you divide 7 by a quantity that isn’t 1 or 7, you’ll not get a the rest of zero.

7 divided by 1 provides a the rest of 0 since 7 = 1 × 7 + 0

7 divided by 2 provides a the rest of 1 since 7 = 2 × 3 + 1

7 divided by 3 provides a the rest of 1 since 7 = 3 × 2 + 1

7 divided by 4 provides a the rest of three since 7 = 4 × 1 + 3

7 divided by 5 provides a the rest of two since 7 = 5 × 1 + 2

7 divided by 6 provides a the rest of 1 since 7 = 6 × 1 + 1

7 divided by 7 provides a the rest of 0 since 7 = 7 × 1 + 0

As illustrated above, solely when 7 is split by 1 and seven will you get a the rest of zero. We will additionally say that the one components of seven are 1 and seven. This provides us a second option to outline a main quantity.

Definition #2: A quantity is prime if the quantity has solely 2 components, 1 and itself.

If the quantity has greater than two components, we are saying that the quantity is composite.

As an example, 12 is a composite quantity as a result of 12 has greater than 2 components. It may be divided by numbers aside from 1 and 12, similar to 2, 3, and 4 which may also be referred to as components.

## A number of fascinating info about prime numbers

- 1 is neither prime nor composite as a result of it has just one issue. Based on the definition, a quantity will need to have no less than 2 components earlier than it may be prime or composite.

- Discover additionally that 2 is the one quantity that’s even and prime on the similar time.

- There are 15 prime numbers lower than 50.

- There are 25 prime numbers lower than 100. Can you discover them?

You should use the definition to check each single quantity. Nonetheless, it’s considerably time-consuming.

As a shortcut, you need to use a technique or algorithm referred to as **Sieve of Eratosthenes**, named after a well-known Greek mathematician.

## Utilizing Sieve’s algorithm to seek out prime numbers between 1 and 50.

- Make an inventory of all numbers from 1 to 50.
- Begin by crossing out 1 as a result of it isn’t prime. Then, circle the subsequent quantity after 1 that’s prime, which is 2.
- Cross out all of the multiples of two till you get to 50, similar to 2, 6, 8, 10, 12…
- Search for the subsequent quantity after 2 that’s prime. That quantity is 3. Circle 3 and cross out all multiples of three, similar to 6, 9, 12, …
- Repeat the method with 5 and seven, and many others. After you’re completed, you need to discover 25 prime numbers.

We present you the method for all numbers from 1 to 50.

The numbers which are circled and never crossed out are the prime numbers. There are 15 prime numbers between 1 and 50.

**Necessary remark:**

The quantity 30 is crossed out by a blue, a crimson, and a inexperienced line. Which means that 30 may be divided by 2, 3 and 5.

Subsequently, the prime numbers lower than 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

## Prime quantity quiz

Take the quiz beneath to see how nicely you perceive this lesson.