Composite numbers
Código FM06-E4800-I
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Composite numbers are numbers that can be written as the multiplication of prime numbers.
For example the number 6, it can be written as 2 times 3, both the number 2 and the number 3 are prime numbers.
The number 9 can be written 3 times 3, and the number 3 is a prime number.
The decomposition of composite numbers is to transform a composite number into the product of prime numbers. And this is for simplifying fractions.
How to decompose the number 12? We see that it is an even number, so the number 2, is the smallest prime number, so we divide the 12 by 2 and we have the number 6, which is also even and can be divided by 2, its division generates the number 3.
The number 3 is odd and also prime, so 3 can only be divided by 3, giving the value 1.
So we have that 12 is the product of 2 times 2 times 3.
And 48, we have that by 2, becomes 24, that by 2 becomes 12, that by 2 becomes 6, that by 2 becomes 3, and 3 is a prime number divided by 3, giving 1.
Now let's do a fraction 48 divided by 12. Now instead of using the number 48 we use the composite decomposed number. And the 12 the same thing.
If we cut the equals at the top into, and at the bottom we have 2 times 2 left over, so the fraction answer is 4.
Now let's do the fraction 195 over 15. Decomposing 195, we have 3 times 5 times 13. And decomposing 15, we have 3 times 5. Cutting the equals at the top and bottom, we have the value 13 left.
If we were to divide 195 by 15 in braces mode, it would be a lot more work. And if the numbers were even higher, it would be a lot more work. So decomposition is much easier to do divisions.
For example the number 6, it can be written as 2 times 3, both the number 2 and the number 3 are prime numbers.
The number 9 can be written 3 times 3, and the number 3 is a prime number.
The decomposition of composite numbers is to transform a composite number into the product of prime numbers. And this is for simplifying fractions.
How to decompose the number 12? We see that it is an even number, so the number 2, is the smallest prime number, so we divide the 12 by 2 and we have the number 6, which is also even and can be divided by 2, its division generates the number 3.
The number 3 is odd and also prime, so 3 can only be divided by 3, giving the value 1.
So we have that 12 is the product of 2 times 2 times 3.
And 48, we have that by 2, becomes 24, that by 2 becomes 12, that by 2 becomes 6, that by 2 becomes 3, and 3 is a prime number divided by 3, giving 1.
Now let's do a fraction 48 divided by 12. Now instead of using the number 48 we use the composite decomposed number. And the 12 the same thing.
If we cut the equals at the top into, and at the bottom we have 2 times 2 left over, so the fraction answer is 4.
Now let's do the fraction 195 over 15. Decomposing 195, we have 3 times 5 times 13. And decomposing 15, we have 3 times 5. Cutting the equals at the top and bottom, we have the value 13 left.
If we were to divide 195 by 15 in braces mode, it would be a lot more work. And if the numbers were even higher, it would be a lot more work. So decomposition is much easier to do divisions.
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Tags
Composite numbers, factoring, decomposing numbers.