Vulgar fractions. Ci 



tiotliing remains, then will the last divisor be the greatest 

 common measure required. 



2. When there are more than two numbers, find tlic 

 greatest common measure of two of them as before ;. and 

 of that common measure and one of the other numbers ; 

 and so on, through all the numbers to the last ; then will 

 the greatest common measure, last found, be the answey, . 



3. If I happen to be the co'mmon measure, the given 

 numbers are prime to each otlicr, and found to be incom- 

 mensurable, 



EXAMPLE*. 



1. Required the greatest common measure of 918, 199S 

 and 522. 

 918)1998(2 So 54 is the greatest common measure 

 1836' _ of 1998 and 918, 



Therefore 18 is the answer required. 



2. What 



Again, since 54 measures 108, and 162, it also measures 



5X162-I-108, or 918. In the same manner it will be found 

 to measure 2X9184-162, or 1998, and so on. Therefore 54 

 measures both 918 and 1998. 



It is also the greatest common measure ; for suppose there be z 

 greater, then since the greater measures 918 and 1998, it also 

 measures the remainder 162 ; and since it measures 162 and 918, 

 it also measures the remainder 108 j in the same manner it will 

 be found to measure the remainder 54 ; that is, the greater meas- 

 ures 



