Math Circles Prime Time Worksheet With Answers - Grade 6 - University Of Waterloo - 2015 Page 5
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10Greatest Common Divisor
The greatest common divisor or GCD of two or more numbers is the largest number that is
a factor of each of the numbers. This can also be called the greatest common factor.
We’re going to examine two different ways of finding the GCD:
Method 1
Find all the factors of each of the numbers and then identify the largest one that is a common
factor of all the numbers. This is the GCD.
Method 2
Begin by finding the prime factorization of each of the numbers. Look at the prime factors
of all the numbers and multiply the ones they have in common. This is the GCD.
Example: Find the GCD of 27 and 18.
Solution:
Using Method 1:
18: 1, 2, 3, 6, 9, 18
27: 1, 3, 9, 27
the GCD is 9.
OR
Using Method 2:
18 = 2
3
3
27 =
3
3
3
the GCD is 3
3 = 9.
Try it out:
Find the GCD of the following groups of numbers.
1. 36 and 64
4
2. 156 and 360
12
3. 328 and 208 and 400
8
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