Which five numbers are prime to 7

Prime numbers

Reading time: 7 min

Prime numbers are natural numbers that are only divisible by and themselves.

For example, the number is only divisible by and and is therefore a prime number.

Let's look at the divisibility of:

So the only factors that divide them are and.

In contrast, the number:

So the factors of the are,, and. It is therefore not a prime number, but a composite number (namely).

Conclusion:

There are numbers that can be broken down into multiplications, they are called "Composite numbers". For example:

And there are numbers that cannot be broken down into multiplications; they are called “prime numbers”. For example:

Other prime numbers are

Let's look at the natural numbers and break them down into factors of other numbers as much as possible.

  • 2not dismantled
  • 3not dismantled
  • 4 can be dismantled into 2 · 2
  • 5 cannot be dismantled
  • 6 can be dismantled into 2 · 3
  • 7 cannot be dismantled
  • 8 can be dismantled into 2 · 2 · 2
  • 9 can be dismantled into 3 · 3
  • 10 can be dismantled into 2 · 5
  • 11 cannot be dismantled
  • 12 can be dismantled into 2 · 2 · 3
  • 13 cannot be dismantled
  • 14 can be dismantled into 2 7
  • 15 can be dismantled into 3 · 5
  • 16 can be dismantled into 2 · 2 · 2 · 2
  • 17 cannot be dismantled
  • 18 can be dismantled into 2 · 3 · 3
  • 19 cannot be dismantled
  • 20 can be dismantled into 2 · 2 · 5
  • 21 can be dismantled into 3 7

The number is missing in the above list, because 1 is not a prime number.

There's up to number in total 25 prime numbers, i.e. numbers that cannot be broken down into multiplications. They are listed below:

By the way, the number is that single even prime number.

All other prime numbers are odd.

If we look at the divisors of the prime numbers, we see that the prime numbers are only divisible by 1 and by themselves. And that is exactly the motto for the prime numbers:

Examples of prime numbers

    Examples of compound numbers

    If there is a natural number next to itself and the 1 further factor, it is one composite number and not a prime number.

      Word origin prime number

      The word “prim” comes from the Latin “prima”, which in turn comes from “primus” and means “first, foremost”. This designation was probably chosen because every natural number consists of prime numbers, they are, so to speak, the atoms of the world of numbers.