the greatest common factor of 12a⁴b⁷ and 185b³
To find the greatest common factor of 12a⁴b⁷ and 185b³, we need to find the largest factor that both terms have in common.
First, let's find the prime factors of each term:
12a⁴b⁷ = 2² * 3 * a⁴ * b⁷
185b³ = 5 * 37 * b³
Now, let's compare the prime factors of both terms:
Common factors:
b³
Therefore, the greatest common factor of 12a⁴b⁷ and 185b³ is b³.
the greatest common factor of 12a⁴b⁷ and 18⁵b³
To find the greatest common factor of 12a⁴b⁷ and 18⁵b³, we need to find the largest factor that both terms have in common.
First, let's find the prime factors of each term:
12a⁴b⁷ = 2² * 3 * a⁴ * b⁷
18⁵b³ = 2 * 3² * a⁰ * b³
Now, let's compare the prime factors of both terms:
Common factors:
2 - both terms have one factor of 2
3 - both terms have one factor of 3
a⁰ - both terms have no factors of a
b³ - both terms have a factor of b³
Therefore, the greatest common factor of 12a⁴b⁷ and 18⁵b³ is 2 * 3 * b³ = 6b³.
Greatest common factor 12a² and 20ab
To find the greatest common factor of 12a² and 20ab, we need to find the largest factor that both terms have in common.
First, let's factorize each term:
12a² = 2 * 2 * 3 * a * a = 2² * 3 * a²
20ab = 2 * 2 * 5 * a * b = 2² * 5 * a * b
Now, let's compare the prime factors of both terms:
Common factors:
2² - both terms have two factors of 2
a - both terms have a factor of 'a'
Therefore, the greatest common factor of 12a² and 20ab is 2² * a = 4a.
Rewrite 2a³b + 6a²b² remove GCF
To rewrite 2a³b + 6a²b² without the greatest common factor, we need to factor out the common factors from each term.
We can factor out an 'a²b' from each term:
2a³b = a²b * 2a
6a²b² = a²b * 6b
So, rewriting 2a³b + 6a²b² without the greatest common factor gives:
a²b(2a + 6b)