Greatest Common Factors?

Question

I understand what a GCF is, and I understand how to find them.
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I hate finding them though, and my brain doesn't want to do it.
Is there an easier way to find these?

363 , 78
What should my first thought be? Second?
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Can someone step me through this? All I do is start listing factors for each, then find the GCF. I hate this cause it takes too much time.
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Is there a trick, or tip that will help me find them QUICKER?
Thanks alot for you help.

Answer 1

In the time, and with the effort, that it took to formulate and write down this question, you could have solved three or four such problems. Discipline is the answer!

Answer 2

There is a ladder method of finding both the GCF and the LCD (Lowest Common Multiple). There is also another way of finding them, too. I don't know what it's really called, but it is like an upside down division sign (something like this: 2____).

My teachings are not that good, since I'm only an 8th grader, but I try my best:
Here's how to work the "upside down division sign" one: Put the factors in the sign, where the "____" is on the "2____" (In this case, put the 363 and the 78 in like this: 363,78 on the bar). Then find out what number(s) go in both of them. Put that number next to the "2" of the sign, and divide. Then write the numbers like ( , ) on the bottom. If there's still some numbers that can go in both of them, make another "upside down division sign" below the previous one. Repeat the dividing until you cannot find any other common numbers between the two numbers. Finally, multiply the numbers that were lined up next to the "2" on the sign. And that will be your GCF!

Answer 3

Yes, sometimes you can find an easy way to get it done.

Generally, you only need to factor the smaller number.

78 = 2*3*13.

Since only 3 divides 363, the GCF = 3.

Answer 4

No there is no trick that I know of. However you mentioned factors. I hope you meant PRIME factors. That should be relatively easy. First Divide by 2 and repeat until 2 cannot be divided, then 3, then 5, then 7, etc.

The only other trick that I know is to write a computer program to find the greatest common factor for you. This way you do the hard work once (writing the program) then you can use it afterwards.

Answer 5

Ok, there is a better way.. my jr. high math teacher taught me. I am pretty sure he just came up with it, and he calls it upside down division:

I'll start with an easy example.. saaaaaay hmm.. 10 and 25.

start with 10
what is the smallest number (besides 1) that goes into ten?
2.. divide 10 by 2. that leaves you with 5
what is the smallest number (besides 1) that goes into five?
five is prime, so it can only be divided by 1 and 5..
5.. divide 5 by 5, you only have one left you are done.

then do 25
what is the smallest number (besides 1) that goes into twenty-five?
5.. divide 25 by 5.. you are left with 5
smallest number into 5 is?
5.. that leaves you with 1.

for ten the numbers we had were: 2 and 5
for 25 the numberts we had were: 5 and 5

now pick the all the numbers that are the same between the two, in this case, there is only one: 5. So your GFC is 5.


You can do it with any numbers.

I will do an example with more then one common number between the two so you can see what to do when that happens.
saaaay.. 36 and 12

start with 36:
2, leaves you with 18
2, that leaves you with 9
3, that leaves you with 3
3, that leaves you with 1

now 12:
2, that leaves you with 6
2, that leaves you with 3
3, that leaves you with 1

for 36: 2 2 3 3
for 12: 2 2 3

3, 2 and 2 are common between the two, so you take those three numbers and multiply them:
3*2*2 = 12. That is your GFC.

Hope that helps!

Answer 6

start with the low #'s to get the higher #s.

for 78 = 2 * 39
78 = 2 * 3* 13
now for 363 (obvious 2 wont work, so go with 3)
363 = 3 * 121 (121 is 11squared)
363 = 3 * 11 * 11 (cant break down any further).

Now you found your number. 3

Answer 7

just prime factor the number
363 = 3x11x11
78 = 2x3x13

look for the common numbers that each number have
3 is the only one so it is the solution.