The First book of Arithmetic

Cover The First book of Arithmetic
The First book of Arithmetic
Dana P Dana Pond Colburn
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To 39 and 54 ? 1|. To 7, 49, and 84 ?
D. A COMMON DIVISOR of two or more numbers is any number which will exactly divide each of them.
ILLUSTRATION. 4 is a common divisor of 4, 8, 12, and 32.
The GREATEST COMMON DIVISOR of two or more numbers is the largest number which is a divisor of each of them. It is also the product of all their common prime factors.
1. What is the greatest common divisor of 24, 36, and 60 ?
SOLUTION. The greatest common divisor of 24, 36, and 60, is the product of all th
...e pfiine factors common to these numbers.
24 = 2x2x2x3 = 2 3 x 3. 36 = 2 x 2 x 3 X 3 = 2* x 3*. 60 = 2x2x3x5 = 2 2 x3x 5.
We see that the only common prime factors are 2, 2, and 3. Hence 2 X 2 X 3, or 12, must be the greatest common divisor required.
108 COLBURN'S FIRST PART.
What is the greatest common divisor 2. Of 30 and 42? 9. Of 4, 6, and 12?
3. Of 4 and 12? 10. Of 3, 9, and 15?
4. Of 8 and 20 ? 11. Of 18, 27, and 45 ? 6. Of 35 and 49 ? 12. Of 14, 28, and 56 ?
6. Of 63 and 72 ? 13. Of 30, 48, and 54 ?


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