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
