![]() We've already seen that the prime factors of 12 are 2 and 3. This means that we can write a number using only the product of its prime factors, and we are allowed to repeat some of them if we need to. So what is prime factorization? Well, there is a theorem in mathematics that says that any integer can be expressed as the product of its prime factors. Prime factors are just a list we want something more. We listed 2 and 3 as the prime factors of 12, but they are NOT the prime factorization of 12. That's just a little different from writing a number's prime factors. It asks you to write the " prime factorization" of a number. It just complicates things that are already complicated enough! Now for your homework. We see here why 1 is not considered as a prime, even though it once was. (We can also include 1, but since it is a factor of every number, it is usually omitted from such lists.) These are the only two prime numbers in the list of the factors of 12, so they are 12's prime factors. For example, what are the prime factors of 12? Answer: 2 and 3. Those are the words what about the phrase? Now, we can combine these two ideas and ask about the prime factors of a number. No other number divides into 7 without leaving a remainder. Now, a prime number is one that has only 2 factors: 1 and itself.įor example, 7 is a prime number, because if we list out all its factors, we only have 1 and 7 on the list. Notice that 5, for example, is not listed, because 12 divided by 5 leaves a remainder. This is because each of these numbers goes into 12 evenly, with no remainder. Could you please help me?Ī factor is an integer that exactly divides a given integer.įor example, if we are given the number 12, we can list its factors as the following: 1, 2, 3, 4, 6, and 12. Now we have a homework sheet that says " Write the prime factorization for each number". The other day while I was gone, my class learned about prime factors. We’ll start with this question from 1997: Prime Factorization The SymPy function to compute ω( n) is called primenu.I’ll close this series on prime numbers by looking at how to find the prime factorization of a number, starting with the most basic ideas applicable to relatively small numbers, and then (next week) looking at some advanced methods for larger numbers. Instead, it computes Ω( n), the number of prime factors of n counted with muliplicity. ![]() SymPy has a function primeomega, but it does not compute ω( n).
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