How to Get Composite Numbers By Using Prime Factorization

Composite numbers are whole numbers larger than one that aren't prime numbers but they can be broken down into prime numbers The process of writing out the prime numbers that make up a composite number is known as prime factorization and every numbers prime factorization is unique. Here are some examples. 6=2x3, 12=2x2x3 or 2squared times three, 250=2x5x5x5 or 2x5cube. 510,510=2x3x5x7x11x13x17, and 42,059=137x307. Okay, so the last one is seducy. Finding that prime factorization without a calculator or a list of primes is tough. The factors of some numbers aren't always obvious but prime factorizations show you the one and only way a number can be factored.

A sleek way of writing out prime factorization is to do upside down division. Let's try it with 120. You put a prime factor or a prime number that evenly divides the number you're working on on the outside left, and the result or quotient which is the number of times it divides evenly underneath. Then, you divide the quotient or the number underneath by another prime number and keep doing this until the bottom number is primed. Then you can---. The order you do this in, it doesn't matter. You get the same result or list of prime factors no matter what order you use. Look at the numbers going down the left side and the number at the bottom. They act the same as divisors in the division problem. But in this case, they're all prime numbers. Although many composite numbers could have been the divisor for 120, the numbers for a prime factorization must all be prime numbers. In this process, you usually do all the two's first than all the three's and five's and so on to make the prime factorization process easier. But you can do this in any order and it works well for larger numbers too. In this case, start with 13 because it seems obvious that it's a factor. The rest are all in mix up order. The prime factorization of 13,000 comes out to 13x5x2x5x2x2x5 or 2cube x 5cube x 13. So that's all there is to it. Now you can break composite numbers down into their lowest prime factors.


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