What is the greatest common factor of 108 and 168?

Question

Also for 65, 104. AND 252, 264

Thanks!

Answer 1

What is the greatest common factor of 108 and 168
65, 104. AND 252, 264

OK, I like to do these by simply finding the (unique) prime factors.
Start by dividing (evenly) by 2 as many times as possible.
Then try dividing by 3, as many times as possible
Then, 5; then 7, 11, 13, etc.
(For large numbers, there is a shortcut using 1001,
since it is the product of 7 x 11 x 13.)

Anyhow, for 108 we have:
2 x 54
2 x 27
3 x 3 x 3
108 = 2^2 x 3^3

And for 168, we have:
2 x 84
2 x 42
2 x 21
3 x 7
7
168 = 2^3 x 3^1 x 7^1

[ANSWER #1]
The common factors of (108, 168) are: 2^2 x 3^1 = 4 x 3 = 12
which gives 12 as the greatest common factor.

----

Now, you ask for 65, 104, and 252, 264.
I'll assume you mean the first two are a pair (65, 104)
and the second two are a pair (252, 264).

[QUESTION #2]
65 =
(no 2 factors): 2^0
(no 3 factors): 3^0
(5 is a factor): 5 x 13
13 is a prime
Therefore 65 = 2^0 x 3^0 x 5^1 x 7^0 x 11^0 x 13^1
or simply 5 x 13

For 104, we have:
2 x 52
2 x 26
2 x 13
so 104 = 2^3 x 13

[ANSWER #2]
Thus, we have 13 as the only common factor for 65 and 104.


[QUESTION 3] 252, 264
Consider 252:
2 x 126
2 x 63
3 x 21
3 x 7
7
So 252 = 2^2 x 3^2 x 7

And for 264:
2 x 132
2 x 66
2 x 33
3 x 11
11
Therefore 264 = 2^3 x 3 x 11

[ANSWER #3]
The common factors (for 252, 264)are: 2^2 x 3
which equals 12.

Answer 2

Are you going to delete this question too after someone works so hard to answer it?

To figure the GCF of two numbers, first figure the prime factors. Take the common ones and multiply them out.

For example 108:
108 / 2 = 54
54 / 2 = 27
27 / 3 = 9
9 / 3 = 3
3 / 3 = 1

So the factors of 108 are 2 x 2 x 3 x 3 x 3

Do the same for 168:
168 / 2 = 84
84 / 2 = 42
42 / 2 = 21
21 / 3 = 7
7 / 7 = 1

The factors of 168 are 2 x 2 x 2 x 3 x 7

The factors they have in common are 2 x 2 x 3

So the GCF(108, 168) is 12

As a double check
12 x 9 = 108
12 x 14 = 168

PROBLEM 2:

65 = 5 x 13
104 = 2 x 2 x 2 x 13

GCF(65, 104) = 13

13 x 5 = 65
13 x 8 = 104

PROBLEM 3:

252 = 2 x 2 x 3 x 3 x 7
264 = 2 x 2 x 2 x 3 x 11

GCF(252, 264) = 2 x 2 x 3 = 12

12 x 21 = 252
12 x 22 = 264

Answer 3

Figure out the primes for each number:

108 = 2 X 2 X 3 X 3 X 3
168 = 2 X 2 X 2 X 3 X 7

The only primes common to both numbers are:

GCF = 2 X 2 X 3 = 12

Answer 4

For 108 and 168 the GCF is 12 as 108 breaks down into 2x2x3x3x3 an 168 brakes down to 2x2x2x3x7 so all the common factors are 2x2x3 which is 12.

For 65 and 104 the GCF is 13 as 65 breaks into 5x13 and 104 is 2x2x2x13. The common factor here is only 13.

For 252 and 264 the GCF is 12 as well as 252 breaks into 2x2x3x3x7 and 264 is 2x2x2x2x3x11. The common factors are 2x2x3 which equals 12.
Hope it helps...

Answer 5

factors
108 = 4(3)(9)
168 = 4(3)(14)
least common factor = 4(3) = 12

factors
65 = 5(13)
104 = 8(13)
least common factor = 13

factors
252 = 4 (3)(21)
264 = 4 (3)(22)
least common factor = 4(3) = 12

Answer 6

gcf of 108 and 168 is 12

Answer 7

Gcf Of 108

Answer 8

12

Answer 9

g.c.f. 108&168 = 12