The fundamental theorem of arithmetic is a theorem in Math that states that every positive integer greater than 1 is either:
– A prime number.
or
– A number that can be formed by the multiplication of prime numbers together.
This theorem is also referred to as the unique factorization theorem.
Fundamental Theorem of Arithmetic in Action
The first six prime numbers areas follows. 2, 3, 5, 7, 11, 13
The following are numbers that are in between these numbers. 4, 6, 8, 9. 10, 12
4 = 2 × 2 ( A prime number multiplied with itself also counts. )
6 = 2 × 3
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
12 = 2 × 2 × 3
And so on.
This can be tried with any positive integer.
33 = 3 × 11
60 = 2 × 2 × 3 × 5 = 22 × 3 × 5
The fundamental theorem of arithmetic also says that the set of prime numbers that do multiply with each other to give a non prime number, will be a unique set.
Thus for 45 and 60 seen above, the prime multiplication displayed is the only one containing prime numbers that will result in 45 and 60.
It’s worth also remembering that the order of the numbers in multiplication doesn’t change anything.
The multiplication 2 × 2 × 3 × 5 is the same as 3 × 2 × 5 × 2.
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