20085

Question

What is the highest common factor of {{algebra1}} and {{algebra2}}?

Worked Solution

Consider each option:

{{solution}}

∴\therefore {{{correctAnswer}}} is the HCF.

Variant 0

DifficultyLevel

570

Question

What is the highest common factor of 6ab6 \large ab and 2b2 \large b?

Worked Solution

Consider each option:

3 is not a factor of 2b2 \large b

2b2 \large b is a factor of both ✓\checkmark

3a3 \large a is not a factor of 2b2 \large b

6ab6 \large ab is not a factor of 2b2 \large b.

∴\therefore 2b2 \large b is the HCF.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
algebra1
$6 \large ab$
algebra2
$2 \large b$
solution
3 is not a factor of $2 \large b$ $2 \large b$ is a factor of both $\checkmark$ $3 \large a$ is not a factor of $2 \large b$ $6 \large ab$ is not a factor of $2 \large b$.
correctAnswer
$2 \large b$

Answers

Is Correct?Answer
x

3

✓

2b2 \large b

x

3a3 \large a

x

6ab6 \large ab

Variant 1

DifficultyLevel

569

Question

What is the highest common factor of 8a8 \large a and 4ab4 \large ab?

Worked Solution

Consider each option:

2b2 \large b is not a factor of 8a8 \large a

8 is not a factor of 4ab4 \large ab

4a4 \large a is a factor of both ✓\checkmark

a\large a is a (smaller) factor of both ✓\checkmark

∴\therefore 4a4 \large a is the HCF.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
algebra1
$8 \large a$
algebra2
$4 \large ab$
solution
$2 \large b$ is not a factor of $8 \large a$ 8 is not a factor of $4 \large ab$ $4 \large a$ is a factor of both $\checkmark$ $\large a$ is a (smaller) factor of both $\checkmark$
correctAnswer
$4 \large a$

Answers

Is Correct?Answer
x

2b2 \large b

x

8

✓

4a4 \large a

x

a\large a

Variant 2

DifficultyLevel

570

Question

What is the highest common factor of 3b3 \large b and 9ab9 \large ab?

Worked Solution

Consider each option:

b\large b is a factor of both ✓\checkmark

3a3 \large a is not a factor of 3b3 \large b

9ab9 \large ab is not a factor of 3b3 \large b

3b3 \large b is a (higher) factor of both ✓\checkmark

∴\therefore 3b3 \large b is the HCF.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
algebra1
$3 \large b$
algebra2
$9 \large ab$
solution
$\large b$ is a factor of both $\checkmark$ $3 \large a$ is not a factor of $3 \large b$ $9 \large ab$ is not a factor of $3 \large b$ $3 \large b$ is a (higher) factor of both $\checkmark$
correctAnswer
$3 \large b$

Answers

Is Correct?Answer
x

b\large b

x

3a3 \large a

x

9ab9 \large ab

✓

3b3 \large b

Variant 3

DifficultyLevel

567

Question

What is the highest common factor of 10bc10 \large bc and 2c2 \large c?

Worked Solution

Consider each option:

10bc10 \large bc is not a factor of 2c2 \large c

5b5 \large b is not a factor of 2c2 \large c

2c2 \large c is a factor of both ✓\checkmark

2 is a (smaller) factor of both ✓\checkmark

∴\therefore 2c2 \large c is the HCF.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
algebra1
$10 \large bc$
algebra2
$2 \large c$
solution
$10 \large bc$ is not a factor of $2 \large c$ $5 \large b$ is not a factor of $2 \large c$ $2 \large c$ is a factor of both $\checkmark$ 2 is a (smaller) factor of both $\checkmark$
correctAnswer
$2 \large c$

Answers

Is Correct?Answer
x

10bc10 \large bc

x

5b5 \large b

✓

2c2 \large c

x

2

Variant 4

DifficultyLevel

571

Question

What is the highest common factor of 4a4 \large a and 20ab20 \large ab?

Worked Solution

Consider each option:

4 is a factor of both ✓\checkmark

4a4 \large a is a (higher) factor of both ✓\checkmark

5b5 \large b is not a factor of 4a4 \large a

20ab20 \large ab is not a factor of 4a4 \large a

∴\therefore 4a4 \large a is the HCF.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
algebra1
$4 \large a$
algebra2
$20 \large ab$
solution
4 is a factor of both $\checkmark$ $4 \large a$ is a (higher) factor of both $\checkmark$ $5 \large b$ is not a factor of $4 \large a$ $20 \large ab$ is not a factor of $4 \large a$
correctAnswer
$4 \large a$

Answers

Is Correct?Answer
x

4

✓

4a4 \large a

x

5b5 \large b

x

20ab20 \large ab