WEBVTT mathematics/basic-math/pyo
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Welcome back; this is a lesson on prime factorization.
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Before we begin, let's go over some terms: prime and composite.
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Prime number we know is a number that has no factors besides 1 and itself.
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For example, the number 5.
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5 only has the factors 1 and itself so that is considered a prime number.
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A composite number is a number that has more factors than 1 and itself.
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For example, the number 10.
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10 is a composite number because we know that the number 2 is a factor of 10 and 5 is a factor of 10.
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So 10 would be considered a composite number.
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A factor then would be all the number parts that go into a given number.
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If we have again 10, the factors would be 1, 2, 5, and 10.
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These are all considered factors of the number 10.
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Product; product is a number where we multiply numbers together.
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The product of 2 and 5 is 10.
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So product, you just multiply the numbers together.
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The method in solving prime factorization is called the factor tree.
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The factor tree... we all know what a tree looks like.
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It is going to branch out into a bunch of factors.
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More specifically, prime factors, which is why it is called prime factorization.
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Let's start off with the number 10.
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I want to break this up into factor pairs; say 5 and 2.
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Once I have a prime number, I want you to circle it.
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We know 5 is a prime number; we know 2 is a prime number.
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Once all the numbers are circled, we know that we have only prime numbers.
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Then we are done; all we have to do is write out the answer.
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10, the prime factorization of 10 would be 5 times 2.
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Another example, 24; 24 has a few different factor pairs.
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You can choose whichever one; let's go with 6 and 4.
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6 and 4, we know that both are not prime numbers.
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They are composite numbers; we have to break them up even further.
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I am going to branch it out again.
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6 is going to break up into 3 and 2.
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This is a prime number; I am going to circle it.
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This is a prime number.
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Then 4, I am going to break up into 2 and 2.
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A prime number, I circle this and that.
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All I have left are prime numbers.
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The prime factorization of 24 would be 3 times 2 times 2 times 2.
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Since I have the same numbers here, I can write this in scientific notation.
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This can be also 3 times 2 to the 3rd power because I have three 2s.
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Here is an example.
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If you can, I want you to pause the video and I want you to try this problem on your own.
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Let's go over this now; 50.
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I am going to break this up into a factor pair; let's say 5 and 10.
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5 is a prime number; circle that one.
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10, I am going to break this up even further to 2 and 5.
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I end up circling those.
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50 becomes 5 times 5 times 2 or I can write it as 5² times 2.
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Here is another example; 15.
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15, I can only break it up into 5 and 3.
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They are both prime numbers; this was an easy one.
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15 becomes 5 and 3; let's do a couple more examples.
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The number 12 becomes 4 and 3; you can also do 6 and 2.
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You are still going to get the same answer.
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3 is a prime number; I am going to circle that one.
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4 becomes 2 and 2; circle those; I have nothing else left.
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The prime factorization of 12 is 2² times 3.
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One more example, 36.
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36, again you have a couple different options; let's go with 6 and 6.
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6, I can break up into 3 and 2; I am going to circle those.
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This 6 also to 3 and 2.
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36 becomes 3 times 3 times 2 times 2.
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This is the same thing as 3² times 2².
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That is it for prime factorization.