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Unit 01 · Whole Numbers and DecimalsLesson

Day 011Greatest Common Factors

LearnClassworkAnswer keyPDF packet ↗
Standards 6.NS.B.4a
LEARNING TARGET

I can find the greatest common factor and interpret equal groups.

01 · LEARN

Build the idea

List factor pairs or use prime factorizations. The greatest factor shared by both numbers is the GCF. For identical kits with no leftovers, the GCF gives the greatest number of kits.

WORKED EXAMPLE 1

Find the GCF of 12 and 16. Show factor pairs or prime factors.

4

Common factors: 1, 2, 4; greatest is 4.

WORKED EXAMPLE 2

Make the greatest possible number of identical kits from 18 pencils and 30 erasers with no leftovers. Find the number of kits and each kit’s contents.

6 kits; 3 pencils and 5 erasers each

GCF(18, 30) = 6; divide both counts by 6.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Find the GCF of 12 and 16. Show factor pairs or prime factors.

  2. Find the GCF of 8 and 12. Show factor pairs or prime factors.

  3. Find the GCF of 10 and 15. Show factor pairs or prime factors.

  4. Find the GCF of 45 and 60. Show factor pairs or prime factors.

  5. Find the GCF of 24 and 36. Show factor pairs or prime factors.

  6. Find the GCF of 18 and 30. Show factor pairs or prime factors.

  7. Make the greatest possible number of identical kits from 60 pencils and 84 erasers with no leftovers. Find the number of kits and each kit’s contents.

  8. Make the greatest possible number of identical kits from 48 pencils and 72 erasers with no leftovers. Find the number of kits and each kit’s contents.

  9. Make the greatest possible number of identical kits from 70 pencils and 100 erasers with no leftovers. Find the number of kits and each kit’s contents.

  10. Make the greatest possible number of identical kits from 12 pencils and 18 erasers with no leftovers. Find the number of kits and each kit’s contents.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. 4

    Common factors: 1, 2, 4; greatest is 4.

  2. 4

    Common factors: 1, 2, 4; greatest is 4.

  3. 5

    Common factors: 1, 5; greatest is 5.

  4. 15

    Common factors: 1, 3, 5, 15; greatest is 15.

  5. 12

    Common factors: 1, 2, 3, 4, 6, 12; greatest is 12.

  6. 6

    Common factors: 1, 2, 3, 6; greatest is 6.

  7. 12 kits; 5 pencils and 7 erasers each

    GCF(60, 84) = 12; divide both counts by 12.

  8. 24 kits; 2 pencils and 3 erasers each

    GCF(48, 72) = 24; divide both counts by 24.

  9. 10 kits; 7 pencils and 10 erasers each

    GCF(70, 100) = 10; divide both counts by 10.

  10. 6 kits; 2 pencils and 3 erasers each

    GCF(12, 18) = 6; divide both counts by 6.

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