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Table of Contents

SECTION III. MULTIPLICATION.

of 87 and 25 is

  • 25) 87 (3
  • 75
  • 12) 25 (2
  • 24
  • 1) 12 (12
  • 12
  • 0

EXERCISES.

Numbers.g. c. m.
619795211
5836326021
55471470084431849
6281326041571
28915314955
15093003093
  • What are 36 × 36 + 2 × 36 × 72 + 72 × 72
  • and 36 × 36 × 36 + 72 × 72 × 72;

and what is their greatest common measure?—Answer, 11664.

  1. If two numbers be divisible by a third, and if the quotients be again divisible by a fourth, that third is not the greatest common measure. For example, 360 and 504 are both divisible by 4. The quotients are 90 and 126. Now 90 and 126 are both divisible by 9, the quotients of which division are 10 and 14. By (87), dividing a number by 4, and then dividing the quotient by 9, is the same thing as dividing the number itself by 4 × 9, or by 36. Then, since 36 is a common measure of 360 and 504, and is greater than 4, 4 is not the greatest common measure. Again, since 10 and 14 are both divisible by 2, 36 is not the greatest common measure. It therefore follows, that when two numbers are divided by their greatest common measure, the quotients have no common measure except
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