i need help well iam learning lcm gcf and so on
i need help well iam learning lcm gcf and so on
Factoring integers is like trying to break down an integer into its different building blocks. And there are a number of little rules that you can memorize that can help you with finding factors other than 1 and the number you want to factor.
For example, if a number is even, then 2 is a factor. So 28 = 14 x 2. But wait! 14 is also even so repeat the rule. 14 = 2 x 7. And we know that we can't break down 2 or 7.
Now, write out what you have: 28 = 2 x 7 x 2. Ahh, we see that our factorization has 2 x 2 = 4, so 4 is also a factor.
Another rule: Lets say you have 3,457,000. Count the number of zeroes, pull them out and throw in a 1:
3,457,000=3457 x 1000. Oh wait, use the first rule again: 1000 = 2 x 500. Oh wait 500 is even, use it again: 500 = 2 x 250. I'm not doing anything exceptionally difficult here except for the simplest thing possible. And I'm repeating it over and over again.
There are other rules that you can memorize that will HELP you do these problems. You still need to do some work when you are learning how to do this stuff.
The way I like to do factoring problems like this is by making a factor tree:
28 Start with the number you are factoring.
14 * 2 Pick any two factors you know.
7*2 Factor these factors.
1 and the number you start with are always factors. The remaining factors can be gleaned from the factor tree - any combination of products of the lowest branches of your tree are factors. Here you have 7, 2, and 2 as your lowest branches. 7*2*2 = (7*2)*2 = 14*2 = 7*(2*2) = 7*4. So your factors in order are 1, 2, 4, 7, 14, and 28.
The factors of 28 are: 1,2,4,7,14 and 28. Rember, the factors of 28 are all of the natural numbers which divide into 28, with no remainder.