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Grade 8 GCF and Equation Quiz

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Questions and Answers

What is the greatest common factor of 24 and 36?

6 (correct)

Which of the following could be a possible equation representing the relationship between x and y if their greatest common factor (GCF) is 9?

$x = 9y$

$xy = 9$

$x + y = 9$

$x - y = 9$ (correct)

What is the greatest common factor of 42 and 56?

14 (correct)

If the greatest common factor of two numbers is 4, what could be a possible equation representing their relationship?

$x - y = 4$ Signup and view all the answers

Which of the following is a plausible equation representing the relationship between two numbers if their greatest common factor (GCF) is 12?

$8x + 12y = 48$ Signup and view all the answers

If the greatest common factor of two numbers is 20, which of the following could be a possible equation representing their relationship?

$28x + 35y = 700$ Signup and view all the answers

If the greatest common factor of two numbers is 18, which equation could represent their relationship?

$6x - 9y = 81$ Signup and view all the answers

Which of the following equations is a possible representation of the relationship between two numbers if their greatest common factor (GCF) is 15?

$12x - 18y = 180$ Signup and view all the answers

If the greatest common factor of two numbers is 25, which of the following could be a possible equation representing their relationship?

$2x + 3y = 25$ Signup and view all the answers

What is the greatest common factor of 36 and 48?

9 Signup and view all the answers

Which of the following equations is a possible representation of the relationship between two numbers if their greatest common factor (GCF) is 28?

$6x + 7y = 28$ Signup and view all the answers

If the greatest common factor of two numbers is 16, what could be a possible equation representing their relationship?

$8x + 8y = 16$ Signup and view all the answers

Study Notes

Greatest Common Factors

The greatest common factor (GCF) of 24 and 36 is 12.
The GCF of 42 and 56 is 14.
The GCF of 36 and 48 is 12.
If the GCF of two numbers is 4, equations could take the form of ( 4x ) and ( 4y ).
If the GCF of two numbers is 9, plausible equations include ( 9a ) and ( 9b ).

Possible Equations Based on GCF

For a GCF of 12, equations might be ( 12m ) and ( 12n ).
If the GCF is 20, valid equations could be ( 20p ) and ( 20q ).
For a GCF of 18, consider equations like ( 18c ) and ( 18d ).
With a GCF of 15, possible representations include ( 15e ) and ( 15f ).
A GCF of 25 leads to equations such as ( 25g ) and ( 25h ).
When the GCF is 16, representations might involve ( 16i ) and ( 16j ).

Summary of Greatest Common Factor Characteristics

The GCF identifies the largest integer that divides two or more numbers without leaving a remainder.
Equations representing a relationship between two numbers, based on their GCF, typically take the form of multiples of the GCF (e.g., ( GCF \cdot m ) and ( GCF \cdot n )).

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Description

Test your knowledge of greatest common factor (GCF) and its relationship with equations. This quiz includes questions about finding the GCF of numbers and identifying possible equations representing the relationship between variables given their GCF.