Question

Greatest common factor 18a⁴b³ and 21a⁸b³

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the greatest common factor of 18a⁴b³ and 21a⁸b³, we need to identify the highest power of each variable that appears in both terms.

The factors of 18 are 1, 2, 3, 6, 9, and 18.
The factors of 21 are 1, 3, 7, and 21.

The common factors of 18 and 21 are 1 and 3.

The highest power of 'a' that appears in both terms is a⁴.
The highest power of 'b' that appears in both terms is b³.

Therefore, the greatest common factor of 18a⁴b³ and 21a⁸b³ is 3a⁴b³.

Answer 2

Greatest common factor 10x⁶y⁴ and 20x⁷y⁸

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the greatest common factor of 10x⁶y⁴ and 20x⁷y⁸, we need to identify the highest power of each variable that appears in both terms.

The factors of 10 are 1, 2, 5, and 10.
The factors of 20 are 1, 2, 4, 5, 10, and 20.

The common factors of 10 and 20 are 1, 2, and 5.

The highest power of 'x' that appears in both terms is x⁶.
The highest power of 'y' that appears in both terms is y⁴.

Therefore, the greatest common factor of 10x⁶y⁴ and 20x⁷y⁸ is 10x⁶y⁴.

Answer 4

Wrong

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake. Let's correct that.

The prime factors of 10 are 2 and 5.
The prime factors of 20 are 2 and 5.

The common factors of 10 and 20 are 2 and 5.

The highest power of 'x' that appears in both terms is x⁶ in the first term and x⁷ in the second term. The greatest common factor of x⁶ and x⁷ is x⁶.
The highest power of 'y' that appears in both terms is y⁴.

Therefore, the greatest common factor of 10x⁶y⁴ and 20x⁷y⁸ is 10x⁶y⁴.

Answer 6

Rewrite 24ab²c + 18a³b factor out the gcf

Answer 7

[AI-generated answer — Bot GPT 3.5]

To factor out the greatest common factor (GCF) of 24ab²c and 18a³b, we need to look for the highest power of each variable that appears in both terms.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
The factors of 18 are 1, 2, 3, 6, 9, and 18.

The GCF of 24 and 18 is 6.

The highest power of 'a' that appears in both terms is a.
The highest power of 'b' that appears in both terms is b.

Therefore, the GCF of the coefficients and variables is 6ab.

Now, we factor out the GCF from each term:
24ab²c = 6ab * 4b²c = 6ab(4b²c)
18a³b = 6ab * 3a² = 6ab(3a²)

Therefore, factoring out the GCF 6ab from 24ab²c and 18a³b results in:
6ab(4b²c + 3a²)

Answer 8

Rewrite 6a² + 12a⁵ factor out GCF

Answer 9

[AI-generated answer — Bot GPT 3.5]

To factor out the greatest common factor (GCF) of 6a² and 12a⁵, we need to identify the highest power of 'a' that appears in both terms.

The factors of 6 are 1, 2, 3, and 6.
The factors of 12 are 1, 2, 3, 4, 6, and 12.

The GCF of 6 and 12 is 6.

The highest power of 'a' that appears in both terms is a² in the first term and a⁵ in the second term.

Therefore, the GCF of the coefficients and variables is 6a².

Now, we factor out the GCF from each term:
6a² = 6a² * 1 = 6a²
12a⁵ = 6a² * 2a³ = 6a²(2a³)

Therefore, factoring out the GCF 6a² from 6a² and 12a⁵ results in:
6a²(1 + 2a³)