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You already know how to find prime factors. The method is called a 'factor tree'. Here's how it works.
Let's start with the composite number 60
Split it into two factors ... numbers that multiply to 60.
You can do it any way you want ... we'll use 2 and 30.
Whenever one of your new factors is a prime number, stop and circle it. Then keep breaking up any numbers that are left...
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We circled the 2. That 'branch' is done.
Since 30 is composite, we kept going.
We chose to split it as 2 and 15.
The 2 is prime, so we'll circle it, but we can keep going with the 15 ...
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The 15 only has factors of 3 and 5.
Circle both of those. Now all the branches end with prime numbers, so we're done.
60 = 2 X 2 x 3 x 5 = 22 x 3 x 5
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Let's try one more. How about 300.
We'll split it as 10 x 30. There are other choices, but they'll all result in the same final answer. As long as the two numbers multiply to 300, they'll work.
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Both the 10 and the 30 are composite, so both branches continue. Let's do the left branch first, and break up 10 as 2 x 5.
Both of these get circled, since they're prime, and this branch ends.
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Working on the other side now, we'll split up the factor 30 as 3 x 10, and circle the 3 because it's prime. Just one branch left to do ...
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... and here's the final result. The 10 splits into the two factors 2 x 5, both prime, and that branch is done. Listing all the circled numbers in order gives us the prime numbers that multiply to 300:
300 = 2 X 2 x 3 x 5 x 5 = 22 x 3 x 52
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So that's how you find the prime factors of a composite number without a special calculator. Remember that the answer that you get is unique; there isn't any other possible answer that will work.
Let's summarize the rule one more time:
Every composite number can be written just one way as the product of prime numbers.
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