16 had a greater measure than 8, it could not be common to 16 and 8.
| Therefore | 8 | is g. c. m. of | 16 and 8, |
|---|---|---|---|
| (97) g. c. m. of | 16 and 8 | is g. c. m. of | 24 and 16, |
| g. c. m. of | 24 and 16 | is g. c. m. of | 112 and 24, |
| g. c. m. of | 112 and 24 | is g. c. m. of | 360 and 112, |
| Therefore | 8 | is g. c. m. of | 360 and 112. |
The process carried on may be written down in either of the following ways:
- 112) 360 (3
- 336
- 24) 112 (4
- 96
- 16) 24 (1
- 16
- 8) 16 (2
- 16
- 0
| 112 | 360 | 3 |
|---|---|---|
| 96 | 336 | 4 |
| 16 | 24 | 1 |
| 16 | 16 | 2 |
| 0 | 8 |
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.
- 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