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Exam Statistics
Average = 49.4/75 ~ 65.9%
Stddev = 11.7 ~ 15.6%
# Tests = 120
Score Range
#people in range
65 75
14
55.64
28
45.54
38
35.44
28
<35
12
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View Full DocumentEuclid’s Algorithm
The Greatest Common Divisor(GCD) of two integers is defined
as follows:
An integer c is called the GCD(a,b) (read as the greatest
common divisor of integers a and b) if the following 2
conditions hold:
1)
c  a
∧
c  b
2) For any common divisor d of a and b, d  c.
Rule 2 ensures that the divisor c is the greatest of all the
common divisors of a and b.
One way we could find the GCD of two integers is by trial and
error. Another way is that we could prime factorize each
integer, and from the prime factorization, see which factors are
common between the two integers. However, both of these
become very time consuming as soon as the integers are
relatively large.
However, Euclid devised a fairly simple and efficient algorithm
to determine the GCD of two integers. The algorithm basically
makes use of the division algorithm repeatedly.
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 Spring '09

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