Download Math 81 Activity # 5

Math 84
Activity # 3
“Greatest Common Factor”
Your Name: ___________________ Team Member #1__________________
Team Member #2.______________ Team Member #3__________________
Find the greatest common factor of 24 and 30.
Method 1: List the factors of 24 and 30.
Factors
Factors
1
24
1
30
2
12
2
15
3
8
3
10
4
6
5
6
The common factors of 24 and 30 are 1, 2, 3, and 6.
What is the greatest common factor? _____
Method 2: Using prime factorization and exponents.
24
2
12
3 4
2 2
Prime factorization is 2  2  2  3
30
3 10
2 5
Prime factorization is 2  3  5
The Fundamental Theorem of Arithmetic states that every integer greater than
1 is either prime or may be uniquely expressed as the product of prime numbers.
We use this theorem to find the greatest common factor (GCF).
1) Use factor trees to find the unique prime factorization of each number (as
seen above)
2) Then use exponential notation to represent the prime factorization.
The prime factorization of 24 is 2  2  2  3  23  31
The prime factorization of 30 is 2  3  5  21  31  51
Observe we place the bases in ascending order (smallest to largest).
3) Write down all the bases they have in common only. 2 3 (we do not repeat
the 2or 3)
4) Write down the smallest exponent per base 21  31
5) Multiply out the product 21  31  6 .
Therefore, 6 is the greatest common factor (GCF) of 24 and 30.
Method 3: Using prime factorization.
Be careful this time, for the greatest common factor we circle the prime factors
in common ONLY.
24:
2
30:
2
2
2
3
3
5
What prime numbers did you circle as a set? ______ Multiply this numbers, the
product is ____.
The Greatest common factor is ____.
To remember this method for GCF try this G C F, circle all the common
prime factors
Problem 1: Find the greatest common factor of 24, 40, and 72.
Find the prime factorization of each number 24, 40 and 72.
24
40
72
Prime factorization is
Prime factorization is
Prime factorization is
_________.
_________.
_________.
Insert all the prime numbers in the appropriate boxes for each number. Start by
putting all the prime numbers for the largest number in this case 72. Then insert
the rest of the numbers, notice the shaded boxes are there to guide you. Circle
the prime numbers that are in common with all three numbers.
24:
40:
72:
What is the GCF of 24, 40 and 72? _____
Problems:
1) Find the factors of 25.
Factors
2) Find the factors of 26.
Factors
3) Find the factors of 64.
4) Find the factors of 24.
Factors
Factors
5) Find the factors of 36.
6) Find the factors of 42.
Factors
Problems:
Factors
Use any method to find the GCF.
1) Find the GCF of 12 and 40.
2) Find the GCF of 14 and 18.
3) Find the GCF of 20 and 36.
4) Find the GCF of 15 and 35.
5) Find the GCF of 14, 18 and 36.
6) Find the GCF of 8, 16, 38.
7) Find the GCF of 120 and 144.
8) Find the GCF of 44 and 105.