Ray's New Practical Arithmetic · Arts. 83–86 · Unit 9: Factoring

47. Factors and prime numbers

Goal: Your child explains factors, multiples, prime and composite numbers, finds the primes to 100 with the book's sieve, and tests for 2, 3 and 5.

⏱ About 35 minutes · 6 steps

Open it at the Internet Archive ↗

You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil

What's in the book

Definitions for factoring (factor, multiple, prime, composite, common factor, G. C. D., L. C. M.), a rule for finding prime numbers by crossing out, the principles of factoring, and quick tests for 2, 3 and 5.

The lesson, step by step

  1. Warm-up

    Ask: What two numbers multiply to make 12? Find as many pairs as you can. (2 × 6, 3 × 4.)

  2. Factors and multiples

    Read:

    Factors of a number are two or more numbers, the product of which equals the given number

    A multiple of a number is a product of which the number is a factor.

    One and the number itself are not considered factors of a number.

  3. Prime and composite

    Read:

    A prime number has no factors.

    A composite number has two or more factors.

    Ask: Is 7 prime? 9? 15? 23?

  4. The sieve

    Read the rule:

    Write the odd numbers in a series 1, 3, 5, 7, 9, etc.

    After 3 erase every 3rd number; after 5 erase every 5th number; after 7 erase every 7th number;

    Then 2 and the numbers that remain are the prime numbers.

    Do the book's exercise together: find the prime numbers from 1 to 100.

  5. Quick tests

    Read:

    Two is a factor of every even number.

    Three is a factor of a number when the sum of its digits is 3 or some multiple of 3.

    Five is a factor of every number whose unit figure is 0 or 5.

    Test 2457 together: 2 + 4 + 5 + 7 = 18, so 3 is a factor.

  6. Wrap-up

    Read the remaining definitions (common factor, G. C. D., L. C. M.) once; they come up in the next guides. Quick-fire: prime or not? 29, 33, 41, 51, 57.

Answers to the book's problems

Primes from 1 to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 (25 primes). Ray's sieve starts from 1 in the list of odd numbers; today 1 is not counted as a prime.

Worked out for this site from the scan. If a number in your copy differs, trust the book.

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