primes include: 2, 3, 5, 7, 11, 13, 17, 19, 23 …

20 = 2 x 2 x 5

Prime Numbers

A Prime Number is a whole number, greater than 1, that can be evenly divided only by 1 or itself. (2,3,5,7,11,13…)

Factors” are the numbers you multiply together to get another number:

For example 12

smallest prime # is 2

12 divided by 2 is 6

6 divided by 2 is 3 and 3 is a prime number

The answer is ======12=2X2X3

YOU HAVE TO MAKE THE LITTLE TREE YOUR TEACHER TAUGHT YOU IN CLASS!!!!!!!!

Heres a prime factorization chart to better help you with your homework

http://www.mathnstuff.com/papers/games/prime.htm

So, 1 and 5 are prime numbers, but 10 = 5 x 2, so it’s not prime, and 20 = 10 x 2, so it’s not a prime number, either.

For example: 2, 3, 5, 7, 11, 13,17, and 19 are the primes under 20

but 6 can be broken down to 2×3 (both primes)

10 is 2X5

20 is 4×5, but 4 isn’t prime. That breaks down to 2×2 so 20 is 2x2x5

24 is 4×6, but 4 is 2×2 and 6 is 2×3 so 24 is 2x2x2x3

every number can be broken down to primes

example. one would be a prime number

1 x 1 =1

2 would be one

2×1 =2

10 would not be one because you can use 5 x 2 to get 10

5 would be one

and 20 would not because you can do

20 x 1

but also

10 x 2

4 x 5

under 20:

0, 1, 2, 3, 5, 7, 11, 13, 17, 19

good luck!

4 a: any of the numbers or symbols in mathematics that when multiplied together form a product; also : a number or symbol that divides another number or symbol b:

In your case, the word “factor” is a technical term with a precise meaning in the field of mathematics; i.e. any number that can evenly divide another number is said to be a factor of that number. E.G. 2 is a factor of 10 because 2 divides 10 evenly with no leftover “remainder”. 2 goes into 10 exactly 5 times. By this same reasoning, 2 is not a factor of 11 because when 2 divides 11, it goes in 5 times, with 1 left over. When we divide 11 by 2 we get 5 1/11. The 1/11 is said to be the “remainder” and if the remainder is not 0, the division was not “even”.

Merriam-Webster goes on to define factorization as:

: the operation of resolving a quantity into factors; also : a product obtained by factorization

In one sense, this process, factorizing, is just one of the many ways mathematics uses to mean the same thing. E.G. In arithmetic, anywhere the number 100 is used, we can replace the number with an operation like 10 x 10, which of course, equals 100. We could also write 500 – 400 which also equals 100. In fact, there are an infinite amount of ways we can write the quantity 100 in arithmetic. But only some of those infinite ways are interesting or useful. But thinking about one number as the product (product being multiplication) of other numbers has lots of uses. E.G. lets say that you and a friend build a go-cart, and then sell it to another friend for $100. Now you want to divide the cash evenly with your friend. Well, since 100 = 50 x 2, you know that if you divide the 100 into 2 piles of 50 each, you have divided it evenly. By converting the way you think about that $100 into thinking about 2 piles of $50 each, it becomes easy to divide it evenly.

Well in mathematical terms, what you did was “factorize” 100 into 50 x 2. This process is called factorization and you have performed a particular “factorization” of 100. There are other possible factorizations, e.g. 25 x 4, or 10 x 10.

Here’s, I think, a cool thing about math, out of all possible factorizations of 100, only one of those factorizations is said to be “prime”; i.e. the Prime Factorization.

This simply means that all of the factors are prime. In other words, each of the numbers in this particular factorization is prime. E.G. we say 10 is a factor of 100 because it evenly divides 100 as we saw (100=10×10), but 10 is not prime.

The dictionary defines “prime number” as:

: any integer other than 0 or ± 1 that is not divisible without remainder by any other integers except ± 1 and ± the integer itself.

Prime numbers are extremely interesting to mathematicians because they are the ONLY numbers that can ONLY be evenly divided by themselves and 1. The vast majority of numbers can be divided evenly by lots of numbers; only the Prime Numbers have this quality. Take our 100 again. It can be evenly divided by 100 to get exactly (evenly) 1, evenly divided by 50 to get exactly 2, divided by 25 to get 4, by 10 to get 10, by 5 to get 20, and by 1 to get 100. So the list of factors of 100 is 1,2,5,10,20,25 and 50. Notice that in this list of factors, only some of the numbers are prime, namely 1,2 and 5.

So far, we have been factorizing 100 into only 2 factors, e.g. 50×2 or 10×10, but in the case of 100, we can factorize it into more than two factors, e.g. 10x5x2=100.

Now for the INCREDIBLE BEAUTY AND POWER OF PRIME NUMBERS !!!

It turns out that every number (rather every positive whole number, or counting number, i.e. positive integers), can be represented by one and only one factorization where all of the factors are prime. The infamous Prime Factorization! It’s guaranteed! Pick any positive integer you like, and you’ll find it has a prime factorization.

This may seem like some way out math nerd stuff, and I suppose it is. But, did you know that all the contemporary security systems that protect all our financial transactions depend on this fact, that every number has a prime factorization? And that the difficulty of breaking, or “hacking” these ciphers is directly related to the difficulty of factoring large numbers. (When math folks talk about the mandatory and unique prime factorization, they shorten it to just ‘factor’, so when some math nerd says they “factored” a number, or the “factors” of a number, it means they are talking about the Prime Factorization.

So for our example of 100, we can approach it in steps like:

Step 1) 100 = 100 x 1

Step 2) 100 = 50 x 2 x 1

Step 3) 100 = 10 x 5 x 2 x 1

Step 4) 100 = 5 x 2 x 5 x 2 x 1

And since the “1” doesn’t make any difference here

100 = 5 x 5 x 2 x 2

Since all the numbers in the above factorization are prime, that is the prime factorial.

For your 20, try 20=10×2=5x2x2.

here is a link to the national library of virtual manipulatives. they have some really great interactive applets to help in math.

be sure you have java enabled on your computer

http://nlvm.usu.edu/en/nav/frames_asid_202_g_3_t_1.html