Ray's New Practical Arithmetic · Art. 89 · Unit 9: Factoring
49. Greatest common divisor
Goal: Your child finds the greatest common divisor of two or more numbers by common factors and by repeated division.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
The principle of the G. C. D., two methods (multiply the common prime factors; divide the greater by the less, again and again), a remark for more than two numbers, and 20 problems with answers.
The lesson, step by step
Warm-up
Ask: What is the biggest number that divides both 12 and 18? (6.)
The principle
Read:
The G. C. D. of two or more numbers contains all the prime factors common to the numbers, and no other factor.
First method
Read:
Find the prime factors common to the given numbers.
Multiply them together.
The product will be the greatest common divisor.
For 30 and 42 the common factors are 2 and 3, so the G. C. D. is 6.
Second method
Read:
Divide the greater number by the less, the divisor by the remainder, and so on,
always dividing the last divisor by the last remainder, until nothing remains.
The last divisor will be the greatest common divisor.
For 30 and 42: 42 ÷ 30 leaves 12; 30 ÷ 12 leaves 6; 12 ÷ 6 leaves 0. G. C. D. 6.
Independent practice
Your child does problems 2 to 10 by the first method and 11 to 17 by the second (which is easier for big numbers like 16571 and 38363).
Check and wrap-up
Answers are printed in a list after the problems. Mental: G. C. D. of 8 and 12? Of 15 and 25? Of 14 and 21?
Tip
The second method (today called Euclid's method) is worth the effort. It works even when the factors are hard to spot.