The rule for finding the greatest common measure of two numbers is,
I. Divide the greater of the two by the less.
II. Make the remainder a divisor, and the divisor a dividend, and find another remainder.
III. Proceed in this way until there is no remainder, and the last divisor is the greatest common measure required.
99. You may perhaps ask how the rule is to shew when the two numbers have no common measure. The fact is, that there are, strictly speaking, no such numbers, because all numbers are measured by 1; that is, contain an exact number of units, and therefore 1 is a common measure of every two numbers. If they have no other common measure, the last divisor will be 1, as in the following example, where the greatest common measure of 87 and 25 is found.
- 25) 87 (3
- 75
- 12) 25 (2
- 24
- 1) 12 (12
- 12
- 0
EXERCISES.
| Numbers. | g. c. m. | |
|---|---|---|
| 6197 | 9521 | 1 |
| 58363 | 2602 | 1 |
| 5547 | 147008443 | 1849 |
| 6281 | 326041 | 571 |
| 28915 | 31495 | 5 |
| 1509 | 300309 | 3 |
- What are 36 × 36 + 2 × 36 × 72 + 72 × 72
- and 36 × 36 × 36 + 72 × 72 × 72;
and what is their greatest common measure?—Answer, 11664.