Lesson 6.7Find Factors and Multiples
Start hereWords, worked example, and sentence starters
Learning target I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.
Why This Matters The station quartermaster has two jobs today. First, split the pencil and notebook stock into identical combo packs with nothing left over — that is a factor question. Second, work out when two supply runs that repeat on different cycles will land in the same week — that is a multiple question. Same lesson, opposite tools. Today the stock is 24 pencils and 36 notebooks. One supply run arrives every 6 days and another arrives every 8 days.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| FactorSpanish: Factor | A whole number that divides another number evenly, with no remainder. | 1, 2, 4, 8, 16 divide 16. |
| MultipleSpanish: Múltiplo | The result of multiplying a number by 1, 2, 3, and so on — where you land when you skip-count by it. | Multiples of 8: 8, 16, 24, 32, 40 … |
| Greatest common factor (GCF)Spanish: Máximo común divisor (MCD) | The largest number that is a factor of two or more numbers. It answers “how many equal groups can I make?” | 48 and 36 share 1, 2, 3, 4, 6, 12 → GCF = 12 |
| Least common multiple (LCM)Spanish: Mínimo común múltiplo (mcm) | The smallest number that is a multiple of two or more numbers. It answers “when will these line up again?” | 6, 12, 18, 24 and 8, 16, 24 → LCM = 24 |
| Factor pairSpanish: Par de factores | Two factors that multiply to make a number. In a word problem, one is the number of groups and the other is the size of each group. | 2 × 12 = 24 |
| Prime factorizationSpanish: Descomposición en factores primos | Writing a number as a product of prime numbers, usually with a factor tree. Multiplying the primes two numbers share also gives the GCF. | 24 = 2 × 2 × 2 × 3 |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Find the GCF of 20 and 30.
- Factors of 20: 1, 2, 4, 5, 10, 20.
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
- Shared factors: 1, 2, 5, 10. The greatest is 10.
Answer: GCF = 10
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A factor tree breaks each number into primes. 48 = 2 × 2 × 2 × 2 × 3, and 36 = 2 × 2 × 3 × 3.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The factors of are .
- The factors that both numbers share are .
- The greatest common factor is .
- I used the GCF here because the problem asks for .
Word bank factorfactor paircommon factorgreatest common factorGCFprimeprime factorizationdivides evenlylistsharegreatestequal groups
Watch out!A common mistake
A common mistake is reaching for the wrong tool: listing FACTORS for a problem about repeating cycles. Ayasha's classes repeat every 6 and 8 weeks, so the weeks they land on are multiples
Lesson 6.7Find Factors and Multiples
Level 0Most support · every hint printed
Learning target I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.
Why This Matters The station quartermaster has two jobs today. First, split the pencil and notebook stock into identical combo packs with nothing left over — that is a factor question. Second, work out when two supply runs that repeat on different cycles will land in the same week — that is a multiple question. Same lesson, opposite tools. Today the stock is 24 pencils and 36 notebooks. One supply run arrives every 6 days and another arrives every 8 days.
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Find the GCF of 20 and 30.
- Factors of 20: 1, 2, 4, 5, 10, 20.
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
- Shared factors: 1, 2, 5, 10. The greatest is 10.
Answer: GCF = 10
-
1Write the name of the correct group on each line.
Sort each number by its relationship to 10.
- 2
- 20
- 5
- 30
- 10
- 50
Steps to try- Check both relationships: does this number divide 10 evenly, and does 10 divide this number evenly?
- A positive factor of 10 divides 10 with no remainder.
- 10 passes both checks, so it belongs in the Both category.
-
2Circle the letter of the best answer. Show how you know.
Which list shows all the factors of 12?
- A1, 2, 3, 4, 6, 12
- B1, 12
- C2, 3, 4, 6
- D12, 24, 36, 48
Steps to try- Ask: what divides 12 with nothing left over?
- Try each number from 1 up to 12.
- Do not forget 1 and the number itself.
Show your work -
3Circle the letter of the best answer. Show how you know.
Which list shows the first four multiples of 8?
- A1, 2, 4, 8
- B2, 4, 6, 8
- C8, 16, 24, 32
- D8, 9, 10, 11
Steps to try- Skip-count by 8 out loud.
- 8 × 1, 8 × 2, 8 × 3, 8 × 4.
- Multiples get bigger; factors stay at or below the number.
Show your work -
4Circle the letter of the best answer. Show how you know.
What is the greatest common factor of 12 and 18?
- A2
- B3
- C6
- D36
Steps to try- List the factors of each number.
- Circle the numbers that appear in both lists.
- Pick the largest circled number.
Show your work
Explain your thinkingBoth problems say “common.” How do you decide whether a problem wants the GCF or the LCM?
Sentence starter If the problem ___ something into equal groups, I use the ___. If it asks when things ___ again, I use the ___.