FInd the greatest common factor of each set of number below by factoring each number as a produt of prime?

Question

HELP ME SUPPER PLEEZ

26,65
70,98
63,84
60,42
30,105,225,42
60,42,66,98
16,24,40,
70,84,112
12,15,36,42
60,96,132,180
HELP PLEEZ>.<

Answer 1

It will be better to teach you the method than to just give you the answers. First you need to understand the meaning of Greatest Common Factor. That is the largest number that divides evenly into both numbers. Don't confuse this with the least common multiple. The greatest common factor of 26 and 65, for example is 13, because they both divide evenly by 13 (2 x 13, 5 x 13).

To figure this out, calculate the prime factors. Do this by starting with 2. Keep dividing by 2 until it no longer divides evenly, then move to 3, etc. until you end up with something that won't divide anymore.

So:
26 / 2 = 13

This won't divide anymore, so the prime factors of 26 are 2 x 13

Similarly for 65:
2 doesn't divide evenly
3 doesn't divide evenly
65 / 5 = 13

This won't divide anymore, so the prime factors of 65 are 5 x 13.

Now compare your two lists of factors, take all the common factors (if there are several, multiply them together), this will give the greatest common factor.

So you can see that the greatest common factor of 26 and 65 is 13.
This can also be written as GCF(26, 65) = 13


Let's try figuring the greatest common factor of 63 and 84. Again, you can write this as GCF(63, 84):

Prime factors of 63:
2 doesn't work, skip to 3
63 / 3 = 21
21 / 3 = 7
And 7 is prime, so the prime factors are 3 x 3 x 7 = 63

Prime factors of 84:
84 / 2 = 42
42 / 2 = 21
2 doesn't work, skip to 3
21 / 3 = 7
And 7 is prime, so the prime factors are 2 x 2 x 3 x 7 = 84

Finally, look at all your prime factorizations:
3 x 3 x 7 = 63
2 x 2 x 3 x 7 = 84

They both have a 3 (but only one three), and they both have a 7. So the common factors are 3 and 7. Multiply together and you get GCF (63, 84) = 21.


I'll take one of the harder ones as another example:
60, 42, 66, 98

Prime factors of 60:
60 / 2 = 30
30 / 2 = 15
Can't divide by 2 any more, so change to 3
15 / 3 = 5
And 5 is prime, so the factors are 2 x 2 x 3 x 5 = 60

Prime factors of 42:
42 / 2 = 21
Can't do 2, skip to 3
21 / 3 = 7
And 7 is prime, so the factors are 2 x 3 x 7 = 42

Prime factors of 66:
66 / 2 = 33
Can't do 2, skip to 3
33 / 3 = 11
And 11 is prime, so the factors are 2 x 3 x 11 = 66

Prime factors of 98:
98 / 2 = 49
Can't do 2, or 3, or 5, skip to 7
49 / 7 = 7
And 7 is prime, so the factors are 2 x 7 x 7 = 98

Finally, look at all your prime factorizations:
2 x 2 x 3 x 5 = 60
2 x 3 x 7 = 42
2 x 3 x 11 = 66
2 x 7 x 7 = 49

The number 2 appears in all four, so circle that. Anything else? Nope, nothing else appears in all four.
So GCF (60, 42, 66, 98) = 2

Answer 2

26,65=13*2;13*5 GCF is 13
70,98=2*7*5;2*7*7 GCF is 14
63,84=3*3*7;3*2*2*7 GCF is 21
60,42=5*2*2*3;2*3*7 GCF is 6
30,105,225,42=2*3*5;3*5*7;3*3*5*5;2*3*7 GCF=3
60,42,66,98=2*3*2*5;2*3*7;2*3*11;2*7*7 GCF=2
16,24,40,=2*2*2*2;2*2*2*3;2*2*2*5 GCF=8
70,84,112=2*5*7;2*2*3*7;2*2*2*2*7 GCF=14
12,15,36,42=2*2*3;3*5;2*2*3*3;2*3*7
60,96,132,180=2*2*3*5;2*2*2*2*2*3;2*2*3*11;2*2*3*3*5







82*2*

Answer 3

Too lazy to do your homework, I see. Lucky for you I had nothing better to do so here it is.

13
14
21
3
3
3
4
14
3
6

Don't call me if you fail though.

Answer 4

13
14
21
3
3
3
4
14
3
6