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Common Core: 6th Grade Math : Find Greatest Common Factor

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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All Common Core: 6th Grade Math Resources

6 Diagnostic Tests 186 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Find Greatest Common Factor

Use the distributive property to express the sum 40+36 $\displaystyle 40+36$ as the multiple of a sum of two whole numbers with no common factor.

Possible Answers:

None of these

4(10+9) $\displaystyle 4(10+9)$

9(10+4) $\displaystyle 9(10+4)$

3(10+9) $\displaystyle 3(10+9)$

10(4+9) $\displaystyle 10(4+9)$

Correct answer:

4(10+9) $\displaystyle 4(10+9)$

Explanation:

The distributive property can be used to rewrite an expression. When we use this property we will identify and pull out the greatest common factor of each of the addends. Then we can create a quantity that represents the sum of two whole numbers with no common factor multiplied by their greatest common factor.

40+36 $\displaystyle 40+36$

In this case, the greatest common factor shared by each number is:

$\text{GCF}=4$ $\displaystyle \text{GCF}=4$

After we reduce each addend by the greatest common factor we can rewrite the expression:

4(10+9) $\displaystyle 4(10+9)$

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Example Question #2 : Find Greatest Common Factor

Use the distributive property to express the sum 16+28 $\displaystyle 16+28$ as the multiple of a sum of two whole numbers with no common factor.

Possible Answers:

7(4+7) $\displaystyle 7(4+7)$

4(4+4) $\displaystyle 4(4+4)$

7(4+4) $\displaystyle 7(4+4)$

4(4+7) $\displaystyle 4(4+7)$

5(4+7) $\displaystyle 5(4+7)$

Correct answer:

4(4+7) $\displaystyle 4(4+7)$

Explanation:

16+28 $\displaystyle 16+28$

In this case, the greatest common factor shared by each number is:

$\text{GCF}=4$ $\displaystyle \text{GCF}=4$

After we reduce each addend by the greatest common factor we can rewrite the expression:

4(4+7) $\displaystyle 4(4+7)$

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Example Question #1 : Find Greatest Common Factor

Use the distributive property to express the sum 28+32 $\displaystyle 28+32$ as the multiple of a sum of two whole numbers with no common factor.

Possible Answers:

5(7+8) $\displaystyle 5(7+8)$

8(7+5) $\displaystyle 8(7+5)$

3(7+8) $\displaystyle 3(7+8)$

None of these

4(7+8) $\displaystyle 4(7+8)$

Correct answer:

4(7+8) $\displaystyle 4(7+8)$

Explanation:

28+32 $\displaystyle 28+32$

In this case, the greatest common factor shared by each number is:

$\text{GCF}=4$ $\displaystyle \text{GCF}=4$

After we reduce each addend by the greatest common factor we can rewrite the expression:

4(7+8) $\displaystyle 4(7+8)$

Report an Error

Example Question #2 : Find Greatest Common Factor

Use the distributive property to express the sum 20+36 $\displaystyle 20+36$ as the multiple of a sum of two whole numbers with no common factor.

Possible Answers:

5(5+9) $\displaystyle 5(5+9)$

9(5+4) $\displaystyle 9(5+4)$

4(5+9) $\displaystyle 4(5+9)$

9(5+9) $\displaystyle 9(5+9)$

5(4+9) $\displaystyle 5(4+9)$

Correct answer:

4(5+9) $\displaystyle 4(5+9)$

Explanation:

20+36 $\displaystyle 20+36$

In this case, the greatest common factor shared by each number is:

$\text{GCF}=4$ $\displaystyle \text{GCF}=4$

After we reduce each addend by the greatest common factor we can rewrite the expression:

4(5+9) $\displaystyle 4(5+9)$

Report an Error

Example Question #3 : Find Greatest Common Factor

Use the distributive property to express the sum 20+25 $\displaystyle 20+25$ as the multiple of a sum of two whole numbers with no common factor.

Possible Answers:

None of these

5(4+5) $\displaystyle 5(4+5)$

3(4+5) $\displaystyle 3(4+5)$

5(5+5) $\displaystyle 5(5+5)$

Correct answer:

5(4+5) $\displaystyle 5(4+5)$

Explanation:

20+25 $\displaystyle 20+25$

In this case, the greatest common factor shared by each number is:

$\text{GCF}=5$ $\displaystyle \text{GCF}=5$

After we reduce each addend by the greatest common factor we can rewrite the expression:

5(4+5) $\displaystyle 5(4+5)$

Report an Error

Example Question #6 : Find Greatest Common Factor And Least Common Multiple: Ccss.Math.Content.6.Ns.B.4

Use the distributive property to express the sum 55+100 $\displaystyle 55+100$ as the multiple of a sum of two whole numbers with no common factor.

Possible Answers:

$\displaystyle 20(11+5)$

$\displaystyle 5(10+20)$

$\displaystyle 55(10+4)$

$\displaystyle 5(11+20)$

$\displaystyle 8(11+20)$

Correct answer:

$\displaystyle 5(11+20)$

Explanation:

55+100 $\displaystyle 55+100$

In this case, the greatest common factor shared by each number is:

$\text{GCF}=5$ $\displaystyle \text{GCF}=5$

After we reduce each addend by the greatest common factor we can rewrite the expression:

$\displaystyle 5(11+20)$

Report an Error

Example Question #7 : Find Greatest Common Factor And Least Common Multiple: Ccss.Math.Content.6.Ns.B.4

Use the distributive property to express the sum 10+15 $\displaystyle 10+15$ as the multiple of a sum of two whole numbers with no common factor.

Possible Answers:

None of these

5(2+3) $\displaystyle 5(2+3)$

2(5+3) $\displaystyle 2(5+3)$

3(2+5) $\displaystyle 3(2+5)$

6(2+3) $\displaystyle 6(2+3)$

Correct answer:

5(2+3) $\displaystyle 5(2+3)$

Explanation:

10+15 $\displaystyle 10+15$

In this case, the greatest common factor shared by each number is:

$\text{GCF}=5$ $\displaystyle \text{GCF}=5$

After we reduce each addend by the greatest common factor we can rewrite the expression:

5(2+3) $\displaystyle 5(2+3)$

Report an Error

Example Question #8 : Find Greatest Common Factor And Least Common Multiple: Ccss.Math.Content.6.Ns.B.4

Use the distributive property to express the sum 10+45 $\displaystyle 10+45$ as the multiple of a sum of two whole numbers with no common factor.

Possible Answers:

3(5+9) $\displaystyle 3(5+9)$

9(2+5) $\displaystyle 9(2+5)$

2(5+9) $\displaystyle 2(5+9)$

3(2+9) $\displaystyle 3(2+9)$

5(2+9) $\displaystyle 5(2+9)$

Correct answer:

5(2+9) $\displaystyle 5(2+9)$

Explanation:

10+45 $\displaystyle 10+45$

In this case, the greatest common factor shared by each number is:

$\text{GCF}=5$ $\displaystyle \text{GCF}=5$

After we reduce each addend by the greatest common factor we can rewrite the expression:

5(2+9) $\displaystyle 5(2+9)$

Report an Error

Example Question #4 : Find Greatest Common Factor

Use the distributive property to express the sum 12+18 $\displaystyle 12+18$ as the multiple of a sum of two whole numbers with no common factor.

Possible Answers:

2(6+3) $\displaystyle 2(6+3)$

None of these

4(5+3) $\displaystyle 4(5+3)$

6(2+3) $\displaystyle 6(2+3)$

3(2+6) $\displaystyle 3(2+6)$

Correct answer:

6(2+3) $\displaystyle 6(2+3)$

Explanation:

12+18 $\displaystyle 12+18$

In this case, the greatest common factor shared by each number is:

$\text{GCF}=6$ $\displaystyle \text{GCF}=6$

After we reduce each addend by the greatest common factor we can rewrite the expression:

6(2+3) $\displaystyle 6(2+3)$

Report an Error

Example Question #5 : Find Greatest Common Factor

Use the distributive property to express the sum 42+18 $\displaystyle 42+18$ as the multiple of a sum of two whole numbers with no common factor.

Possible Answers:

7(7+3) $\displaystyle 7(7+3)$

6(5+3) $\displaystyle 6(5+3)$

6(7+3) $\displaystyle 6(7+3)$

3(7+6) $\displaystyle 3(7+6)$

6(4+3) $\displaystyle 6(4+3)$

Correct answer:

6(7+3) $\displaystyle 6(7+3)$

Explanation:

42+18 $\displaystyle 42+18$

In this case, the greatest common factor shared by each number is:

$\text{GCF}=6$ $\displaystyle \text{GCF}=6$

After we reduce each addend by the greatest common factor we can rewrite the expression:

6(7+3) $\displaystyle 6(7+3)$

Report an Error

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Common Core: 6th Grade Math : Find Greatest Common Factor

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #1 : Find Greatest Common Factor

Example Question #2 : Find Greatest Common Factor

Example Question #1 : Find Greatest Common Factor

Example Question #2 : Find Greatest Common Factor

Example Question #3 : Find Greatest Common Factor

Example Question #6 : Find Greatest Common Factor And Least Common Multiple: Ccss.Math.Content.6.Ns.B.4

Example Question #7 : Find Greatest Common Factor And Least Common Multiple: Ccss.Math.Content.6.Ns.B.4

Example Question #8 : Find Greatest Common Factor And Least Common Multiple: Ccss.Math.Content.6.Ns.B.4

Example Question #4 : Find Greatest Common Factor

Example Question #5 : Find Greatest Common Factor

All Common Core: 6th Grade Math Resources

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