How do you find the GCF for numbers that have variable?
ex. 35a^2,85ab
How do you find GCF of 8 and 12:
8=2*2*2
12=2*2*3
You look for all possible factors that are common for the two numbers, namely 2*2.
Same for expressions:
35a²=5*7*a*a
85ab = 5*17*a*b
Can you find the GCF now?
Would this be 5*a^3?
No its not.
The factors that are common should be counted only once, like the 5 you counted only once.
a appears twice in the first expression, but only once in the second, so you count the minimum times it occurred, namely once.
So the common factor is 5a.
7, 17, and b do not have common factors in both expressions.
Thank you very much.
You're very welcome!
To find the greatest common factor (GCF) for numbers that have variables, you can follow these steps:
Step 1: Identify the variables shared by both terms.
In this case, the variables are "a" and "b".
Step 2: Determine the highest power or exponent of each variable.
For 35a^2, the highest power of "a" is 2.
For 85ab, the highest power of "a" is 1, and the highest power of "b" is 1.
Step 3: Find the common factors.
Find the factors that both terms share by evaluating the lower powers (or exponents) of each variable. The common factors for "a" are 1 and 1 (from the exponents 2 and 1). The common factors for "b" are 0 and 1 (from the exponents 0 and 1).
Step 4: Determine the GCF.
To determine the GCF, take the product of the common factors for each variable. In this case, the GCF for "a" is 1 (1 x 1) and the GCF for "b" is 1 (0 x 1). Therefore, the GCF for 35a^2 and 85ab is 1.
Alternatively, you can also express the terms in their prime factorization form, then identify the common factors. However, for this particular example, the steps explained above should be sufficient.