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If you know that a number is divisible by three, then you know that three and the number that results from the dividing are both factors of the original number. If you know that a number is not divisible by three, then you won't waste time performing that function. It's rare that the first factor other than one isn't a number between two and ten. If you know the divisibility rules, it will make factoring easier and faster.
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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 the divisibility rules help find prime factorization?
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.
Is 350 composite or prime?
350 is a composite number. it can be divisible by 10, 35, 5, 2 etc. You will find it easier to tell between prime and composite if you know the divisibility rules. one simple one is that if a number ends with zero it is divisible by 10...there are a lot of other divisibility rules.
Would you rather find all the factors of a number or find all the prime factors of a number?
Once all the prime factors of a number have been found, the number of factors the number has and what they are can be found. I'd be finding the prime factors first before finding all the factors of a number, so I'd rather find all the prime factors as it means I can stop before I have to do more work in finding all the factors.
How do you find factors of number 1757051?
The factors of 1757051 are: 1, 1291, 1361, 1757051
