Write the prime factorization of these numbers.
54
150
48
64
75
132
1
Two students made factor trees of the prime factors of 24. Are both correct? Explain why or why not.
Sarah
Kerry 24
24
3
4
2
2
6
3
8
2
4
2
2
2
2
Using Prime Factorization to find the GCF:
1) List the prime factorization of both numbers.
2) Find the product of all of the common factors.
Ex. Find the GCF of 24 and 36.
24 = 2 x 2 x 2 x 3
36 = 2 x 2 x 3 x 3
GCF = 2 x 2 x 3 = 12.
3
Using Prime Factorization to find the LCM:
1) Write the prime factorization of the numbers.
2) Count the number of times each prime number appears in each of the factorizations.
3) For each prime number, take the largest of the counts.
4)Write down that prime number as many times as you counted in step 3.
5) Find the product of the numbers you just wrote down.
Ex. Find the LCM of 8 and 12.
Step 1
8 = 2 x 2 x 2
12 = 2 x 2 x 3
Step 2
2 occurs 3 times
2 occurs 2 times
3 occurs 1 time
Step 3
2 occurs 3 times
3 occurs 1 time
Steps 4 and 5
2 x 2 x 2 x 3 = 24. 24 is the LCM
4
Using Prime Factorization to find the GCF and the LCM
a. 100 = 2 x 2 x 5 x 5
100 = 2 x 2 x 5 x 5
120 = 2 x 2 x 2 x 3 x 5 120 = 2 x 2 x 2 x 3 x 5 GCF =
b.
LCM =
27 = 54 =
GCF =
LCM =
c.
48 =
54 =
GCF =
LCM =
d. 75 = 150 = GCF = LCM = 5