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Greatest Common Factor
Definition: The Greatest Common Factor is the largest
number that will divide into two other numbers or the
number that contains all the factors common to both
numbers.
Example: the Greatest Common Factor of 2940 and
3150 is found by finding all the prime numbers they
have in common and multiplying them.
2940: 2 x 2 x 3 x 5x7x7
3150:2x3x3x5x5x7
You can see that the numbers in red are what they have
in common therefore the Greatest Common Factor is
2x3x5x7 =210
Least Common Multiple
• Definition: The Least Common Multiple is the smallest
number that two numbers will divide into. In other words
all of the factors of the two numbers have to be used.
• An example of the Least Common Multiple of 2940 and
3150 are as follows.
• 2940: 2 x 2 x 3 x 5x7x7
• 3150:2x3x3x5x5x7
• Therefore the LCM is found by multiplying
• 2x2x3x3x5xrx7x7 = 44100
• Caution do not overuse a factor. Don’t count both top and
bottom just the maximum times it appears in either the top
or bottom.
Factor
• To factor a number means to break it up into
numbers that can be multiplied together to
get the original number.
• Example 14 = 7x2 so 7 and 2 are factors of 14.
Prime Number
• A prime number is a natural number greater
than 1 that has no positive divisors other than
one or itself.
• Examples include 7 and 13.
Composite Numbers
• Composite Numbers are numbers that are
Natural Numbers greater than one and not
prime.
• Examples include 8, and 9.
Natural Numbers
• Natural numbers: There is some debate as to
whether natural numbers include zero or not,
but basically they are the positive numbers
and do not include fractions.
Practice
Find the LCM and GCF for each set of
numbers
1) 250
332
2)630
358
3) 276
912
4) 77
11