Prime Factors, LCM and GCF Review
Prime Number: _______________________________________________________________________
_________________________________________________________________________________________
Composite Number: __________________________________________________________________
__________________________________________________________________________________________
Factor trees show us _________________________________________________________________
Find the Prime Factors of 1080
Find the Prime Factors of 8500
Write the prime factors for the factor trees in Exponent Form:
________________________________________
_______________________________________
LCM and GCF
1) The _____________________________________________ is the largest ____________________
that two or more numbers share.
2) The _____________________________________________ is the smallest ___________________
that two or more numbers share.
- Greatest Common Factor –
The product of all of the prime factors
that the numbers have in common will
tell us their GCF.
- Least Common Multiple Each prime factor is multiplied by the
number of times it is a factor in the
factor tree it appears the most.
Note: There are other ways of finding the GCF and LCM. The method you use is
up to you. Refer to your class notes to see the other methods.
Find the GCF of 210 and 252
Find the LCM of 60 and 54
Find the GCF of 270 and 198
Find the LCM of 315 and 420
Simplifying Fractions Using the GCF
-A fraction is fully simplified when there are no common ____________________ in
the numerator and denominator.
-The greatest common factor of the numerator and denominator tells us the
_____________________ of all the common factors.
-We can ____________________ both the numerator and denominator by the GCF to
find a fully simplified fraction.
Examples
Fully simplify the fractions given below:
120
420
1260
2625
Adding or Subtracting Fractions Using the LCM
-To add or subtract fractions, the denominators must be ________________________.
-The least common multiple will tell us the smallest number we can multiply
both denominators by to get a common number.
-Multiply the numerator by the same number as the denominator.
13 5 65   7 4 28  65  28 93

Ex: The LCM of 12 and 15 is 60, so     +     
.
60
60
12 5 60  15 4 60 
Examples
Add/subtract the fractions given below:
10 21

27 45
161 97

168 100
Word Problems Involving GCF and LCM
1) Use the GCF for word problems that:
a) ________________________________________________________________________________
b)_______________________________________________________________________________
Ex: There are 85 snickers bars and 51 lollipops. What is the largest number of
treat bags that can be made if the snickers and lollipops are divided equally?
2) Use the LCM for word problems that:
a)________________________________________________________________________________
b)________________________________________________________________________________
c)_______________________________________________________________________________
Ex: What is the smallest square pizza we can make if the pizza must be cut into
10cm x 12cm rectangular pieces without any leftover parts?
Using Prime Factors to Identify Perfect Squares and Cubes
1) If the prime factors of a number can be divided into ________ _______________
groups, then the number is a perfect _____________________. The square ____________
of the number is _________ of the groups of prime factors.
Ex: Is 1156 a perfect square? What is its square root?
2) If the prime factors of a number can be divided into _________ _________________
groups, then the number is a perfect ____________________. The cube _______________
of the number is ____________ of the groups of prime factors.
Ex: 1728 a perfect cube? What is its cube root?