Since <math><mstyle displaystyle="true"><mn>21</mn><mi>c</mi><mi>d</mi><mo>,</mo><mo>-</mo><mn>3</mn><mi>d</mi></mstyle></math> contain both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numeric part then find GCF for the variable part.

Steps to find the GCF for <math><mstyle displaystyle="true"><mn>21</mn><mi>c</mi><mi>d</mi><mo>,</mo><mo>-</mo><mn>3</mn><mi>d</mi></mstyle></math> :

1. Find the GCF for the numerical part <math><mstyle displaystyle="true"><mn>21</mn><mo>,</mo><mo>-</mo><mn>3</mn></mstyle></math>

2. Find the GCF for the variable part <math><mstyle displaystyle="true"><msup><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>,</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>,</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msup></mstyle></math>

3. Multiply the values together

Find the common factors for the numerical part:

The factors for <math><mstyle displaystyle="true"><mn>21</mn></mstyle></math> are all numbers between <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>21</mn></mstyle></math> , which divide <math><mstyle displaystyle="true"><mn>21</mn></mstyle></math> evenly.

Check numbers between <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>21</mn></mstyle></math>

Find the factor pairs of <math><mstyle displaystyle="true"><mn>21</mn></mstyle></math> where <math><mstyle displaystyle="true"><mi>x</mi><mo>⋅</mo><mi>y</mi><mo>=</mo><mn>21</mn></mstyle></math> .

List the factors for <math><mstyle displaystyle="true"><mn>21</mn></mstyle></math> .

The factors for <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> are all numbers between <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> , which divide <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> evenly.

Check numbers between <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math>

Find the factor pairs of <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> where <math><mstyle displaystyle="true"><mi>x</mi><mo>⋅</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</mn></mstyle></math> .

List the factors for <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> .

List all the factors for <math><mstyle displaystyle="true"><mn>21</mn><mo>,</mo><mo>-</mo><mn>3</mn></mstyle></math> to find the common factors.

The common factors for <math><mstyle displaystyle="true"><mn>21</mn><mo>,</mo><mo>-</mo><mn>3</mn></mstyle></math> are <math><mstyle displaystyle="true"><mn>1</mn><mo>,</mo><mn>3</mn></mstyle></math> .

The GCF for the numerical part is <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Next, find the common factors for the variable part:

c,d,d

The factor for <math><mstyle displaystyle="true"><msup><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msup></mstyle></math> is <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> itself.

c

The factor for <math><mstyle displaystyle="true"><msup><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msup></mstyle></math> is <math><mstyle displaystyle="true"><mi>d</mi></mstyle></math> itself.

d

List all the factors for <math><mstyle displaystyle="true"><msup><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>,</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>,</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msup></mstyle></math> to find the common factors.

The common factor for the variables <math><mstyle displaystyle="true"><msup><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>,</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>,</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msup></mstyle></math> is <math><mstyle displaystyle="true"><mi>d</mi></mstyle></math> .

d

The GCF for the variable part is <math><mstyle displaystyle="true"><mi>d</mi></mstyle></math> .

Multiply the GCF of the numerical part <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and the GCF of the variable part <math><mstyle displaystyle="true"><mi>d</mi></mstyle></math> .

Do you know how to Find the GCF 21cd-3d? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.