Identify the greatest common factor of 12a^4b^7 and 18a^5b^3.
5 answers
The greatest common factor of 12a^4b^7 and 18a^5b^3 is 6a^4b^3.
What is the greatest common factor of 12a^2 and 20ab
To find the greatest common factor of 12a^2 and 20ab we need to find the largest number and the highest power of each variable that divides evenly into both numbers.
The prime factors of 12 are 2 * 2 * 3
The prime factors of 20 are 2 * 2 * 5
The greatest common factor of 12 and 20 is 4 (2 * 2)
For the variables:
The highest power of a that divides evenly into both 12a^2 and 20ab is a^1
The highest power of b that divides evenly into both 12a^2 and 20ab is b^0 (since there is no b term in 12a^2)
Therefore, the greatest common factor of 12a^2 and 20ab is 4a.
The prime factors of 12 are 2 * 2 * 3
The prime factors of 20 are 2 * 2 * 5
The greatest common factor of 12 and 20 is 4 (2 * 2)
For the variables:
The highest power of a that divides evenly into both 12a^2 and 20ab is a^1
The highest power of b that divides evenly into both 12a^2 and 20ab is b^0 (since there is no b term in 12a^2)
Therefore, the greatest common factor of 12a^2 and 20ab is 4a.
Rewrite the expression 2a^3b + 6a^2b2 by factoring out the GCF.
To factor out the greatest common factor (GCF) from the expression 2a^3b + 6a^2b^2, we need to find the largest common factor of both terms.
The GCF of the coefficients 2 and 6 is 2.
The variables have a^2 in common and the term with the lowest power of b is b. Therefore, the GCF of a^3b and a^2b^2 is a^2b.
Factor out the GCF from both terms:
2a^3b + 6a^2b^2 = 2a^2b(a + 3b)
The GCF of the coefficients 2 and 6 is 2.
The variables have a^2 in common and the term with the lowest power of b is b. Therefore, the GCF of a^3b and a^2b^2 is a^2b.
Factor out the GCF from both terms:
2a^3b + 6a^2b^2 = 2a^2b(a + 3b)