Ray's New Practical Arithmetic · Arts. 87–88 · Unit 9: Factoring
48. Prime factors and common factors
Goal: Your child breaks a number into its prime factors by dividing, and finds the prime factors two or more numbers share.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
How to resolve a number into prime factors, 43 numbers to factor, then how to find the prime factors common to two or more numbers, with problems. Answers are printed.
The lesson, step by step
Warm-up
Mental: 30 ÷ 2? 15 ÷ 3? Is 5 prime?
The rule
Read:
Divide the given number by any prime number that will exactly divide it.
The several divisors and the last quotient will be the prime factors of the given number.
Work:
Resolve 30 into its prime factors.
30 ÷ 2 = 15; 15 ÷ 3 = 5, a prime. So 2, 3 and 5.
A factor tree
Show 48 as a tree: 48 = 2 × 24 = 2 × 2 × 12 = 2 × 2 × 2 × 6 = 2 × 2 × 2 × 2 × 3. The book uses repeated short division, which gives the same answer.
Common factors
Read:
To find the prime factors common to two or more numbers.
Work the book's example: What prime factors are common to 30 and 42? Divide both by 2 (15 and 21), then by 3 (5 and 7). 5 and 7 share nothing, so 2 and 3 are the common factors.
Independent practice
Your child factors about 15 of the 43 numbers (mix small and large, such as 36, 48, 105, 154, 2310), then does common-factor problems 2 to 8.
Check and wrap-up
Answers are printed. Mental: prime factors of 12? of 18? What do they share? (2 and 3.)