Find the GCF of 14abc and 28a^2 b^2 c^3
How do I answer this??
find the highest power of primes and variables that divide both terms:
14abc = 14abc
28a^2b^2c^3 = 14abc * 2abc^2
So, the GCF is 14abc
It divides both terms, but no higher powers of anything will do so.
To find the greatest common factor (GCF) of 14abc and 28a^2b^2c^3, we need to identify the common factors and determine which one is the greatest.
First, let's break down the two expressions into their prime factors:
14abc = 2 * 7 * a * b * c
28a^2b^2c^3 = 2 * 2 * 7 * a * a * b * b * c * c * c
Next, we can find the common factors by comparing the prime factors of both expressions:
Common factors:
- The number 2 appears twice in both expressions.
- The number 7 appears once in both expressions.
- The variable 'a' appears once in both expressions.
- The variable 'b' appears once in both expressions.
- The variable 'c' appears once in both expressions.
Now, to find the GCF, we multiply the common factors:
GCF = 2 * 7 * a * b * c = 14abc
So, the GCF of 14abc and 28a^2b^2c^3 is 14abc.