how would i solve this GCF equation?

Question

56x^4y^2z and 49x^2z^2

Answer 1

This is not an equation... I take it that you want to find the Greatest Common Factor of

... 56 x^4 y^2 z and 49 x^2 z^2.

For every variable, look for the smallest power.
... of x^4 and x^2, x^2 is smallest.
... of y^2 and (nothing), (nothing) is smallest
... of z and z^2, z is smallest
Also, the least common factor of 56 and 49 is 7.

Therefore, the solution is
... 7 x^2 z.

Answer 2

Determine the highest factor shared between both terms

56x^4y^2z = 2* 2 * 2 * 7 * x* x* x* x* y* y* z
49x^2z^2 = 7 * 7 * x * x* z * z

The factors shared between both are 1 7, 2 x's, and 1 z. Therefore, the GCF is 7x^2z.

Enjoy!

Answer 3

7x^2 z is it.
This is found by finding the greatest common factor of each term, then combining them.

56 = 7 * 8, and 49 = 7 * 7, so this part is 7

x^4 = x^2 * x^2 and the other is just x^2, so use the x^2

There is no y term in the second one, so you dont have a y as a common factor.

The first term has z and the second is effectively z * z, so you only can use the lowest exponent, or the z.

Put it all together, and you get 7x^2 z as your GCF.

Answer 4

56x^4 y^2 z = 2^3 * 7 * x^4 *y^2 * z
49x^2z^2 = 7^2 * x^2 z^2
GCF = 7 * x^2 * z least. powers of common factors (only)

Answer 5

Numbers first, 56 and 49:

Factors of 56 are 1,2,4,7,8,14,28,56
Factors of 49 are 1,7, and 49
GCF of these is 7

Factors of x^4 and x^2:
Factors of x^4 are 1,x,x^2, x^3, and x^4
Factors of x^2 are 1,x, and x^2
GCF of these is x²

No common factors for y, since there are none in 49x²z²

Factors of z and z²:
Factors of z are 1 and z
Factors of z² are 1, z, and z²
GCF of these is z

Total GCF is thus: 7x²z

Answer 6

56x^4y^2z = 7x^2z(8x^2y^2)
49x^2z^2 = 7x^2z(7z)
So GCF = 7x^2z

Answer 7

(x^2)z