How many factors does 36

Prime numbers, divisors and multiples

In this article we clarify what is hidden behind prime numbers and prime factorization. To do this, we also deal with common divisors and multiples of numbers.

Most of the students in school are not initially clear why they do things like that Prime numbers, Prime factorization or Divider and Multiples of numbers needed. The answer is, these things will be needed in future math lessons. For example, when calculating fractions, it makes sense to reduce the fractions. And to do this, you have to know what the common factors are. It is particularly worthwhile to deal with this article if you do not want to worry about fractions afterwards.

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Prime numbers

A Prime number is a number that is only divisible by 1 or by itself with no remainder. So, please read through this sentence 3-5 times and think about it. Because that's the whole secret behind prime numbers. Let's take a small example to make it clearer: The number 11. This number cannot be divided by 2, 3, 4, 5, 6, 7, 8, 9, 10, 12 or any other number without a remainder / decimal point arises. The number 11 is only divisible by 1 and itself - i.e. 11. This makes the number 11 a prime number. As well as the following numbers:

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 ....

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Prime factorization

The prime factorization is used to convert a number into the smallest possible products. Or to put it another way: to break down a number into the smallest possible multiplications of prime numbers. This can best be shown using examples.

Example 1:

  • 24 = 2 · 12
  • 24 = 2 · 2 · 6
  • 24 = 2 · 2 · 2 · 3
  • The numbers 2 and 3 are the prime numbers

Example 2:

  • 90 = 2 · 45
  • 90 = 2 · 5 · 9
  • 90 = 2 · 5 · 3 · 3
  • The numbers 2, 3 and 5 are the prime numbers

Divisors and multiples: greatest common divisor (gcd)

In this section we deal with the greatest common factor, called GCF for short. In doing so, two numbers are "broken down" and examined to determine which number is the largest possible. This, too, can best be understood with the help of examples.

Example 1 (numbers 6 and 12):

  • The divisors of 6: 1, 2, 3, 6
  • The divisors of 12: 1, 2, 3, 4, 6, 12
  • The number 6 is the largest number that occurs in both factors

Example 2 (numbers 36 and 48):

  • Divisors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  • Divisors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  • The number 12 is the largest number that occurs in both factors


To think again: We find the divisors for both numbers. For this purpose, it is checked by which number can be divided without leaving a remainder / a decimal point. Once all the factors have been found, a look is made to see which is the largest number that can be found for both factors.

Divisors and multiples: Least common multiple (LCM)

We are still missing the smallest common multiple, called LCM for short. Here again two numbers are considered. The respective number is multiplied by 2, 3, 4 etc. and written down in a row. Then a look is given to where the lowest common number can be found.

Example 1 (LCM of 6 and 18):

  • Multiples of 6: 6, 12, 18, 24 ....
  • Multiples of 18: 18, 36, 54 ....
  • The smallest common number is therefore 18.

Example 2 (LCM of 12 and 18):

  • Multiples of 12: 12, 24, 36, 48, 60 ....
  • Multiples of 18: 18, 36, 54, 72, 90 ...
  • The smallest common number is therefore 36.

Exercises / written exams

That with divisors, multiples etc. can be practiced very well in fractions, because this is exactly where it is applied. So if you want to practice, take a look at our fraction calculation area.

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