So we can write that 75 is 3 times 5 times 5. So 75 is 3 times something else. Every other whole number can be broken down into prime number factors.

Prime numbers Video transcript Write the prime factorization of We could keep going. So then we could try 3. Does 3 go into 75? What is the prime factorization of ? So 75 is equal to 3 times 5 times 5. Example The prime factors of are 2, 3, 5 and If you want to know more, the subject is "encryption" or "cryptography".

So 2 is a prime number. So we have a couple of interesting things here. Then if you move to 10, 10 is also not prime, divisible by 2 and 5. What is the prime factorization of 17?

So if you take the digits 2 plus 5, you get 7. Here are some examples: Unique And here is another thing: So this is a prime factorization, but they want us to write our answer using exponential notation. So what is 5 times 5? Prime Factorization "Prime Factorization" is finding which prime numbers multiply together to make the original number.

And it must be a whole number greater than 1. The first few prime numbers are: This idea can be very useful when working with big numbers, such as in Cryptography. In fact this idea is so important it is called the Fundamental Theorem of Arithmetic.

And we could keep going on like this. And 3 is a prime number, so we have the answer:As an example, let's write the prime factorization of Well, = 36_ Since neither 36 nor 10 is a prime number, we are not done.

36 = 9_4 and 10 = 2_5. 2 and 5 are both prime, so we have part of the answer. Drawing factor trees is a good way of doing prime factorization. You can make different factor trees to find the same prime factorization. Look at the two examples below. and both give the same prime factorization.

Other Examples of Factor Trees.

shows 2 x 3 x 5 as the prime factorization of Prime Factorization We showed you how to do the factorization by starting at the smallest prime and working upwards.

48 = 8 × 6, so we write down "8" and "6" below Now we continue and factor 8 into 4 × 2. Then 4 into 2 × 2. And lastly 6 into 3 × 2. Prime Factorization. To factor a number is to break that number down into smaller parts.

To find the prime factorization of a number, you need to break that number down to. When using this process, you usually do all the 2s first, then all the 3s, then all the 5s, and so on to make the prime factorization process easier, but you can do this in any order: Here are some examples of how to write out the.

Prime Factorization by Trial Division. Say you want to find the prime factors of using trial division. Start by testing each integer to see if and how often it divides and the subsequent quotients evenly.

The resulting set of factors will be prime since, for example, when 2 is exhausted all multiples of 2 are also exhausted.

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