A prime number is a number that is divisible only by 1 and itself. A number is divisible by another number when the remainder is zero.

For example, 7 is a prime number because 7 is only divisible by 1 and 7. This means that if you divide 7 by a number that is not 1 or 7, you will not get a remainder of zero.

7 divided by 1 gives a remainder of 0 since 7 = 1 × 7 + 0

7 divided by 2 gives a remainder of 1 since 7 = 2 × 3 + 1

7 divided by 3 gives a remainder of 1 since 7 = 3 × 2 + 1

7 divided by 4 gives a remainder of 3 since 7 = 4 × 1 + 3

7 divided by 5 gives a remainder of 2 since 7 = 5 × 1 + 2

7 divided by 6 gives a remainder of 1 since 7 = 6 × 1 + 1

7 divided by 7 gives a remainder of 0 since 7 = 7 × 1 + 0

As illustrated above, only when 7 is divided by 1 and 7 will you get a remainder of zero. We can also say that the only factors of 7 are 1 and 7. This gives us a second way to define a prime number.

Definition #2: A number is prime if the number has only 2 factors, 1 and itself.

If the number has more than two factors, we say that the number is composite.
For instance, 12 is a composite number because 12 has more than 2 factors. It can be divided by numbers other than 1 and 12, such as 2, 3, and 4 which can also be called factors.

You can use the definition to test every single number. However, it is somewhat time-consuming.
As a shortcut, you can use a method or algorithm called Sieve of Eratosthenes, named after a famous Greek mathematician.

We show you the process for all numbers from 1 to 50.

The numbers that are circled and not crossed out are the prime numbers. There are 15 prime numbers between 1 and 50.

Important observation:

The number 30 is crossed out by a blue, a red, and a green line. This means that 30 can be divided by 2, 3 and 5.

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

Take the quiz below to see how well you understand this lesson.

Jun 09, 23 12:04 PM

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