Elements of Algebra

CHAP. VII. OF ALGEBRA. 149 452. But when the two numbers have a common divisor, it is found, and even the greatest which they have, by the following Rule: Divide the greater of the two numbers by the less; next, divide the preceding divisor by the remainder; what remains in this second division will afterwards become a divisor for a third division, in which the remainder of the preceding divisor will be the dividend. We must continue this operation till we arrive at a division that leaves no remainder; and this last divisor will be the greatest common divisor of the two given numbers. Thus, for the two numbers 576 and 252. $252) 576 (2$ $504$ $72) 252 (3$ $216$ $36) 72 (2$ $72$ $0.$ So that, in this instance, the greatest common divisor is 36. 453. It will be proper to illustrate this rule by some other examples; and, for this purpose, let the greatest common divisor of the numbers 504 and 312 be required. $312) 504 (1$ $312$ $192) 312 (1$ $192$ $120) 192 (1$ $120$ $72) 120 (1$ $72$ $48) 72 (1$ $48$ $24) 48 (2$ $48$ $0.$