Egypt Primary 5 Mathematics, Week 5: Factor or multiple? Choosing the right tool

Prime factors, common factors and common multiples

Week 5 · Prime factors, greatest common factor and least common multiple · 3 lessons

Factor or multiple? Choosing the right tool

Discover Mathematics P5: Term 1, Unit 2, Lessons 6–10

GoalDecide whether a problem needs a factor (GCF) or a multiple (LCM), and solve it.

New words

factor problem · a problem about splitting into equal parts or groupsmultiple problem · a problem about repeating, or about when things happen together again

Explanation

Factors and multiples look alike, but they do different jobs. Factors split a number into smaller equal parts, so they are used to share, group or cut with nothing left over, and the GCF gives the biggest equal part. Multiples grow, so they are used when something repeats or when we need a number that fits both of two sizes, and the LCM gives the first time they meet. Ask: am I breaking a number into smaller equal pieces (factor, GCF), or am I building up to a number that two jumps share (multiple, LCM)? Check the answer: a GCF is never greater than either number, and an LCM is never smaller than either number.

Factor / GCF	Multiple / LCM
share equally, nothing left	happens again together
biggest equal pieces	smallest number that fits both
answer is smaller	answer is bigger

Worked examples

Karim has 30 pencils and 45 erasers. He makes identical sets with nothing left over. This is sharing, so use the GCF. GCF of 30 and 45 is 15. He makes 15 sets, each with 30 ÷ 15 = 2 pencils and 45 ÷ 15 = 3 erasers.

One baker packs rolls in boxes of 12 and another in boxes of 18. What is the smallest number of rolls that both can pack in full boxes? This is about a number that fits both sizes, so use the LCM. Multiples of 18: 18, 36. 36 is a multiple of 12 (12 × 3). So 36 rolls: 3 boxes of 12 or 2 boxes of 18.

A floor is 60 cm by 84 cm. Which is the biggest square tile that covers it with no cutting? The side must divide both 60 and 84, so use the GCF. 60 = 2 × 2 × 3 × 5 and 84 = 2 × 2 × 3 × 7, so the GCF is 2 × 2 × 3 = 12 cm. The floor needs (60 ÷ 12) × (84 ÷ 12) = 5 × 7 = 35 tiles.

Class activity

Sort the stories. Write six short problems on cards, three about sharing or cutting into equal parts and three about repeating events (for example, two lights that blink at different speeds). Mix the cards. The child sorts them into “factor” and “multiple” and solves one from each pile with small numbers.

Practice

Factor or multiple? (a) Arranging 36 chairs in equal rows. (b) Two lights blink every 5 s and every 7 s; when do they blink together again? (c) Cutting ropes of 48 m and 72 m into equal pieces as long as possible.

Find the GCF of 48 and 72. How long is each piece in (c) above?

Find the LCM of 10 and 15.

Karim has 18 red beads and 24 blue beads. He makes identical bracelets using all the beads. What is the greatest number of bracelets, and what is on each?

A bus leaves a stop every 15 minutes and a microbus every 20 minutes. They leave together at 8 o’clock. After how many minutes do they next leave together?