Do the prime factor decomposition means to write that number as the multiplication of prime numbers.
You Prime numbers are those who are divisible just by 1 and by himself. So, they are prime numbers: 2, 3, 5, 7, 11, 13, 17, 19,...
Note, then, how the decomposition into prime factors of the numbers 12, 21 and 50 looks like:
12 = 2.2.3
21 = 3.7
50 = 2.5.5
Writing the numbers this way is very useful when we need to calculate, for example, O least common multiple. But how do we decompose into prime factors?
Prime factor decomposition
To decompose into prime factors, we follow a few steps:
- We divide the given number by its smallest prime divisor;
- We divide the quotient by its smallest prime divisor;
- We repeat this process until we get the number 1 as the quotient.
Example: Decompose the numbers below into prime factors:
The) 16
Let's always start with the smallest prime number, which is 2.
Is 16 divisible by 2? Yes.
16 ÷ 2 = 8
The quotient is 8. Is the number 8 divisible by 2? Yes.
8 ÷ 2 = 4
The quotient is 4. Is the number 4 divisible by 2? Yes.
4 ÷ 2 = 2
The quotient is 2. Is the number 2 divisible by 2? Yes.
2 ÷ 2 = 1
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The quotient is 1, so we stop there.
Therefore, 16 = 2.2.2.2
B) 45
45 is divisible by 2? Do not. Let's go to the next prime number, 3.
45 is divisible by 3? Yes.
45 ÷ 3 = 15
The quotient is 15. Is the number 15 divisible by 2? Do not. Is it divisible by 3? Yes.
15 ÷ 3 = 5
The quotient is 5. Is the number 5 divisible by 2? Do not. Is it divisible by 3? Do not.
Is it divisible by 5? Yes.
5 ÷ 5 = 1
The quotient is 1, so we stop there.
Therefore, 45 = 3.3.5
Practical method of decomposition into prime factors
The practical method of decomposing into prime factors is to use a bar and place the results of the divisions one below the other.
On the left side of the bar we put the quotients, on the right side, the prime numbers we are dividing by. When we get to quotient 1, we finish the decomposition.
Example: Decompose the number 110 into prime factors.
Therefore, 110 = 2.5.11.
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