Answer:
Step-by-step explanation:
You want the greatest common factor of ...
- 792x⁹y¹³z⁴
- 1056x⁴yz⁵
- 220x¹²y⁶z²
Greatest common factor
You can factor the coefficients and then identify common factors. Euclid's algorithm offers another way. We can start by finding the smallest difference between the numbers:
1056 -792 = 264
Both these numbers are divisible by 264, so that value is their GCF. The GCF of all three coefficients will be the GCF of 264 and 220. Again, the difference is ...
264 -220 = 44
Both these numbers are divisible by 44, so 44 is the GCF of all three coefficients:
s = 44
Variables
The GCF of the variable constellations will be the product that has each variable to the lowest degree present.
- x has degrees 9, 4, 12, so x⁴ is the greatest common factor
- y has degrees 13, 1, 6, so y is the greatest common factor
- z has degrees 4, 5, 2, so z² is the greatest common factor
The greatest common factor of all three monomials is ...
GCF = 44x⁴yz²
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Additional comment
Euclid's algorithm for the GCF has you find the remainder of the division of the larger number by the smaller, until that remainder is zero. When the remainder is non-zero, it replaces the larger number.
1056 ÷ 792 = 1 r 264
792 ÷ 264 = 3 r 0 . . . . . . . 264 is the GCF of 792 and 1056
When the numbers are close in value, the remainder is simply their difference, as we used above.
