How to Find Prime Factors of a Number
In mathematics, there are prime numbers and composite numbers. Prime numbers are numbers that are only divisible by 1 and itself; for example, 5 is a prime number. Composite numbers are numbers that are divisible by 1, itself and other numbers; for example, 12 is divisible by itself, 1, 2, 3, 4 and 6. If you're looking for a number's prime factors, you're looking for the smallest prime numbers that can be divided into the number you are given. Finding the prime factors of a number can seem tricky, but a few steps will help you find your answer.
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Instructions
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Start with the number you need to find the prime factors for. Let's say your number 2,277.
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Divide 2,277 by the first prime number (which is two). If 2 goes into 2,277 evenly, then you can break up the next number:
2,277 / 2 = 1,138.5
Therefore, 2 does not go in the number evenly. Try 3:
2,277 / 3 = 759
Three goes into 2,277 evenly, now work on 759.
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Divide 759 by the smallest prime number. Two, again, does not go evenly into 759, so try 3:
759 / 3 = 253
Three goes into the number evenly, now work on 253.
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Divide 253 by the smallest prime number. You'll notice that 253 doesn't go into any of the numbers except one:
253 / 11 = 23
Both 11 and 23 are prime numbers, which means you've (almost) come to the end of the road. Now you need to write the prime factors of 2,277 correctly.
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Recall what numbers you used to factor the number 2,277: 3, 3, 11, 23. Mathematically, this is written as 3 x 3 x 11 x 23.
Now, reduce the 3 x 3 to 3 squared to get your final answer.
The prime factors are:
3^2 x 11 x 23
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References
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