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You can test successive prime numbers to see if your number is divisible by them, but knowing the divisibility rules will help you eliminate some steps, depending on what your number is.
If your number is odd, you don't have to test for 2.
If the sum of your number's digits do not total a multiple of 3, you don't have to test for 3.
If your number doesn't end in a 5 or 0, you don't have to test for 5.
Just by looking at your number, you can include or eliminate the three most common primes if you know the rules of divisibility.
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How can you use divisibility rules to help you find the prime factorization of numbers?
Just knowing the divisibility rules for the first four prime factors (2, 3, 5 and 7) will help find the prime factorizations of a large percentage of the numbers you will encounter. At the very least, dividing your original number by those factors should cut it down to a manageable size. The first thing you do when starting a prime factorization is notice whether the number is even. If it is, you can take out two as a factor. If not, you can skip over it. The same with 3 and 5. If you know they are not factors just by looking at the number, it saves a lot of trial and error.
How can disibility rules help you find the prime factorization of 513?
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What is the prime factorization of 268?
find the prime factorization of 268
Find the prime factorization of 560?
Prime factorization of 560 = 2x2x2x2x5x7.
Find The prime factorization of 32?
Prime factorization of 32 is 2x2x2x2x2 (or 25).
