Week 10 · Factors, primes and multiples · 3 lessons
2
Sharing fairly with the greatest common factor
Discover Mathematics P4: Term 1, Unit 6, Lessons 1–6
GoalFind common factors and the greatest common factor (GCF) and use it to share things fairly.
New words
common factor · a number that is a factor of two or more numbersgreatest common factor (GCF) · the biggest of the common factorsshare fairly · to give every group the same amount of each thing
Explanation
Two numbers can have factors in common. To find them, list the factors of each number and circle the ones that are in both lists. The biggest one is the greatest common factor. Sherif has 24 pencils and 36 erasers and wants to make identical gift bags with nothing left over. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. The common factors are 1, 2, 3, 4, 6 and 12, so the GCF is 12. He can make 12 bags, each with 2 pencils and 3 erasers. A Venn diagram shows the common factors in the middle. The GCF tells the greatest number of identical groups.
Worked examples
Factors of 24 and 36. Common factors are in the middle: 1, 2, 3, 4, 6 and 12. The greatest is 12. Check: 24 ÷ 12 = 2 pencils and 36 ÷ 12 = 3 erasers in each of 12 bags.
Find the GCF of 18 and 30. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Common factors: 1, 2, 3, 6. The GCF is 6.
Marwan has 16 red beads and 40 blue beads. He makes the most identical necklaces with no beads left. Factors of 16: 1, 2, 4, 8, 16. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. The GCF is 8, so he makes 8 necklaces, each with 2 red and 5 blue beads.
Class activity
Fair gift bags. Count out 18 beans and 12 buttons. Put them into identical piles so that every bean and every button is used. Find the largest number of piles, and say what is in each pile.
Practice
1
Find the common factors of 12 and 18, and the GCF.
