How do I find the GCF's of these following problems...
1) 36, 81, 27
2) 15, 17, 30
3) 3x^2y, 9x^2
4) 8a^2b, 14ab^2
%) 3cd^4, 12c^3d, 6c^2d^2
I already know 1 and 2...but I am so confused on how to do the last three :/
5.
3 * c * d * d * d *d
4 * 3 * c * c * c * d
2 * 3 * c * c * d * d
they all have 3
they all have c
they all have d
so
3 c d
ooooohhhh okay....I think I'm starting to understand it a little more.
So would #3 be 6xy?
3 would be 3 x^2
3) 3x^2y, 9x^2
3 * x * x * y
and
3 * 3 * x * x
3*x*x is common to both
ugh! Okay let me try again...#4
8a^2b= 2*4*a*a*b
14ab^2= 2*7*a*b*b
They both have 2 in common
They both have a in common
They both have b in common
So....
2ab?
To find the GCF (Greatest Common Factor) of a set of numbers or algebraic expressions, you need to determine the largest number or term that divides evenly into all of them.
1) GCF of 36, 81, 27:
To find the GCF, you can start by looking for common factors of the three numbers and identifying the largest one. In this case, the common factors of 36, 81, and 27 are multiples of 3: 1, 3, 9. Among these, 9 is the largest common factor, so the GCF is 9.
2) GCF of 15, 17, 30:
Similarly, you can identify the common factors of 15, 17, and 30. They are 1 and 5. The largest common factor is 5, so the GCF is 5.
3) GCF of 3x^2y, 9x^2:
In algebraic expressions, you search for the highest power of each variable that appears in all of them. Look at the coefficients and variables separately:
- Coefficients: The GCF of 3 and 9 is 3.
- Variable x: The highest power of x that appears in both terms is x^2.
- Variable y: Only one term contains y, so the highest power is y^1.
Therefore, the GCF of 3x^2y and 9x^2 is 3x^2y.
4) GCF of 8a^2b, 14ab^2:
For algebraic expressions with multiple variables, again we need to find the highest power of each variable that appears in all terms.
- Coefficients: In this case, the GCF of 8 and 14 is 2.
- Variable a: The highest power of a that appears in both terms is a^1.
- Variable b: The highest power of b is b^2 in one term and b^1 in the other.
Therefore, the GCF of 8a^2b and 14ab^2 is 2ab.
5) GCF of 3cd^4, 12c^3d, 6c^2d^2:
Following the same process, we search for the highest power of each variable:
- Coefficients: The GCF of 3, 12, and 6 is 3.
- Variable c: The highest power of c that appears in all terms is c^2.
- Variable d: The highest power of d is d^4 in one term, d^1 in another, and d^2 in the last term.
Thus, the GCF of 3cd^4, 12c^3d, and 6c^2d^2 is 3c^2d.