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THE NEW STUDENT'8 REFERENCE  WORK

2171

A convenient way of finding the greatest common factor is as follows: Arrange the numbers and divide by the smallest prime factor. In the illustration, the smallest prime factor is 2, and the quotients are 12 and 18. Repeat the process, dividing by 2. The quotients are 6 and 9. Divide these quotients by 3, the smallest common prime factor. The quotients, 2 and 3, have no common factor.

The greatest common factor (G. C. F.) of two or more numbers is the product of their common prime factors. In this example the G. C. F. is the product of 2, 2, and 3, which is 12.

EXERCISE 18.

Find the G. C. F. of

1.   24 and   48

2.   36 and   40

3.   64 and    72

4.   75 and   90

5.   48 and 128

6.   36,  40,  48,  72

7.   16,  20,  24,  40

8.   15,  35,  75,  90

9.   18,  36,  72,  90 10.    14;  28,  42,  84

The greatest common factor is often called the greatest common divisor, or the greatest common measure. Finding the G. C. F. of large numbers is of little importance.

CANCELLATION.

Cancelling or striking out common factors from both divisor and dividend does not change the quotient, but it shortens the work in division. Multiply 240 by 24 and divide the product by 20.

Eegular Way                                      Short Way

240                                           12

24                                        J340X24

-—288

960 480

20)5760

288

Cancellation is a method of work that should be employed on every possible occasion.

EXERCISE 19. Cancellation:

1.     6X21X 5- 7X2

2.   40X24X 3—10X12

3.     5X66X 8— 4XH

4.   12X 6X25— 5X18X10

5.     6X24X54- 9X12

6.     7X 8X44-f- 7XHX16

7.   18X30X48—24X30X36

8.   32X50X72-^12X64X70

9.   14X25X36—12X 5X7 10. 28X70X98—20X14X49

2) 24—36

2)12—18 3)6— 9

2— 3