What is the GCF of these sets?

Question

Here's the problem:

308q^8r^6t^2 AND 364q^2r^4s^6t^8


Thank you so much in advance! This is 10 percent of my final grade!

Answer 1

The greatest common factor, or GCF, is the greatest factor that divides two numbers. To find the GCF of two numbers:

List the prime factors of each number.

Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

308 = 2x2x7x11
364 = 2x2x7x13

GCF = 2x2x7 = 28

Between q, r, s, & t, the GCF is q^2r^4t^2

total GCF = 28q^2r^4t^2

Answer 2

308 = 2*154 = 2*2*77=2*2*7*11
364 = 2*182 = 2*2*91=2*2*7*13

so the GCF of 308 and 364 is 2*2*7 = 28

Now, find the GCF of q^8r^6t^2 AND q^2r^4s^6t^8:

q^2 * r^4 * t^2

Now put the two together for the final answer:

28 * q^2 * r^4 * t^2

now what do I get for completing %10 of your final grade?

Answer 3

Hi,
The answer is this:
28q^2r^4t^2

If you have difficulty finding the GCF on expressions like this, you might try lining the similar factors up like this: (Ignore the dots, they're only to maintain spaces.)
308...q^8...r^6............t^2
364...q^2...r^4...s^6....t^8
Now, pick out the variables that appear in both expressions and with the smallest exponents. That's this:
q^2r^4t^2
Finally, find the GCF of 308 and 364.
I assume you know how to do that, but you can find the prime factors of each number:
308 prime factors: {2,2,7,11}
364 prime factors: {2,2,7,13}
Now, pick out the common factors. That's this:
2²*7 = 28
Now, put them all together to find the answer.
28q^2r^4t^2

FE

Answer 4

308 = 2 * 2 * 7 * 11
364 = 2 * 2 * 7 * 13

GCF of 308 and 364 is 2 * 2 * 7 or 28

GCF of q^8 r^6 t^2 and q^2 r^4 s^6 t^8 is q^2 r^4 t^2

so
GCF of 308q^8r^6t^2 AND 364q^2r^4s^6t^8 is
28 q^2 r^4 t^2

Answer 5

308q^8r^6t^2 AND 364q^2r^4s^6t^8
hint: 308 and 364 are divisible by 28
(11 * 28)(q * q * q * q * q * q * q * q)( r * r * r * r * r *r)(t * t)
and
(13 * 28)(q * q)( r * r * r * r)(s * s * s * s * s * s)(t * t * t * t * t*t*t*t)
so (28)(q * q)( r * r * r * r)(t * t)
28q^2r^4t^2 is the GCF