Factors “Factors” are the numbers you multiply together to get another number: “Prime Factorization” is finding which prime numbers multiply together to make the original number.
Why do we need to find the prime factors?
We can’t factor any more, so we have found the prime factors. Why find Prime Factors? A prime number can only be divided by 1 or itself, so it cannot be factored any further! Every other whole number can be broken down into prime number factors. It is like the Prime Numbers are the basic building blocks of all numbers.
Why is prime factorization so important in cryptography?
Cryptography. Cryptography is the study of secret codes. Prime Factorization is very important to people who try to make (or break) secret codes based on numbers. That is because factoring very large numbers is very hard, and can take computers a long time to do. If you want to know more, the subject is “encryption” or “cryptography”.
How to find the smallest prime number in a factorization tree?
So now that we know what a prime is, a prime factorization is breaking up a number, like 75, into a product of prime numbers. So let’s try to do that. So we’re going to start with 75, and I’m going to do it using what we call a factorization tree. So we first try to find just the smallest prime number that will go into 75.
How to find the factorization of a number?
The first way you can use a factor tree to find the factorization of a number is to divide out prime numbers only. Let’s factor 24 using this method. Since 24 is an even number, the first prime number that can be factored out is a 2. This leaves us with 2 * 12. Again, 12 is an even number, so we can factor out another 2, leaving us with 2 * 2 * 6.
How is a factor tree used to find factorization?
Both methods start out with a factor tree. A factor tree is a diagram that is used to break down a number into its factors until all the numbers left are prime. The first way you can use a factor tree to find the factorization of a number is to divide out prime numbers only.
