Question

i came up with 16 would that be correst for the gcf for 8 and 32

Answer 1

gcf or gcd or hcf all stand for the same idea. GCD or greatest common divisor (if u call gcf its greatest common factor) of 2 or more numbers is the greatest common factor of them. Actually, the name explains it all!
Suppose you have 2 numbers 15 and 25. What are the prime decompositions of those 2 numbers? 15=5*3*1 and 25=5*5*1. There are 2 common factors 1 and 5. Select the greatest of them i.e. 5. Its the GCD!
For 8 and 32 GCD=8

Answer 2

thank you i still have a long way to go and im still tryin to figure it out

Answer 3

I didnt understand u. Long way?
See 8=8*1 and 32=8*4. So 8 is a common factor and its the greatest. So its the GCD.
I can make your long way short, if u ask me ur doubts:)

Answer 4

so let me kno if im doing this right okay? my next set of numbers are 64 and 16 and the answer i got is 8

Answer 5

Nope...you are closer but think of 16. Its a common factor for both 16 and 64, and its obviously the greatest of the common factors. 8 is no doubt also a common factor but 16 is greater than 8. so GCD=16.

Answer 6

Do you know the Euclidean Algorithm for computing the GCD? It can be easier to find GCD mechanically. Its a systematic algorithm to find gcd of 2 numbers.

Answer 7

no im sorry i dont, do you mind if you explain it to me? the reason being i still have 22 more sets of numbers haahahaaha

Answer 8

okay...see the moment you don't understand just let me know. Suppose you have 2 numbers 16 and 64. Their GCF can be written as (16,64). This is just a notation, no need to panick! Now, Euclid's algorithm says (16,64)=(16,64-16)=(16,48) i.e. you can just subtract any of the 2 numbers from the other, but the GCD remains the same! Again (16,48)=(16,32)=(16,16)=(16,0). I just subtracted one from another in a series of steps until I get one number 0. The number beside 0 is the gcd! So (16,64)=(16,0)=16 is the GCD!

Answer 9

ok i think i got it but tell me if im right on the next two set of number the first set is 76 and 57 and would the gcf be 19 and the second set is 86 and 36 and the answer i got is50 is that right

Answer 10

For (8,32)=(8,32-8)i.e.(8,24)=(8,24-8)i.e.(8,16)=(8,16-8)i.e.(8,8)=(8,8-8)i.e.(8,0)=8. So GCD=8! for 8 and 32. Simple, isnt it?
Observe that you can perform this whole series in 1 step: (8,32)=(8,32-4*8)=(8,0)=8. I subtracted from 32 4 times 8, instead of subtracting 4 times in 4 steps, I just did it at once!

(76,57)=(76,76-57)=(76,19)=(76-4*19,19)=(0,19)=19. You are right!
(86,36)=(86-2*36,36)=(14,36)=(14,36-2*14)=(14,8)=(6,8)=(6,2)=(2,2)=(2,0)=2. I think you are wrong here.

Answer 11

well i tried again subtracting 88 and 66 the answer i got is 22 is this correct

Answer 12

Ok...see...For computing the gcf of 88 and 66, what you do is subtract 88 from 66 and write it in this form: (to write in this form is essential!)
(88,66)=(88,22). But you cant stop here! ONLY when you get one number of the pair as 0, ONLY THEN you can stop and tell the answer. (88,22) CAN BE REDUCED FURTHER. See this:
(88,22)=(66,22) I subtracted 22 from 88.
Again (66,22)=(44,22) I subtracted 22 from 66.
Again (44,22)=(22,22) I subtracted 22 from 44.
Again (22,22)=(22,0) I subtracted 22 from 22.
NOW I CAN STOP since I have a 0 in the pair. The other number i.e. 22 is the GCD.

So you are correct. Please show your working for the next step, to be sure u understood.
:)

Answer 13

34,51=34-51,17
17-51=34
is this correct?

Answer 14

the gcf i hav is 17

Answer 15

(34,51)=(51,17)=(34,17)=(17,17)=(17,0)=17. You are correct!

Answer 16

i did the next one of 93 and 39 and i came up with 1 is that possible

Answer 17

(93,39)=(54,39)=(15,39)=(39,24)=(15,24)=(15,9)=(7,9)=(7,2)=(5,2)=(3,2)=(1,2)=(1,1)=(1,0)=1. You are right.
When 2 numbers have GCD=1 we call those numbers coprime numbers. These numbers are very interesting.

Answer 18

I hope you understood. If you have further doubts, you can read what I have told you in previous posts. Hope I could make your "long way" short! :)
I need to be going now from here. Good luck!

Answer 19

thank you