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Activity 1 The Greatest Common Factor
jOb ective Determine the greatest common factor of two numbers.
1. Textbook Instructions Activity 1 The Greatest Common Factor
This activity introduces more systematic and Go over these two methods of finding the GCF of two numbers.
efficient methods of determining the greatest Have students choose the method that is easier for them to follow.
common factor of two numbers.
Learn how to find the greatest common factor.
Method 1: Use prime factorization.
First, the method of prime factorization is Method 1 Use prime factorization.
introduced. The prime factors of a single
number are determined by progressively Find the greatest common factor of 6 and 12.
decomposing its factors.
Find the prime factorization of 6 and 12.
Example: 6 and 12.
6 at once yields the prime factors 2 and 3. 12 6=2 3 12 = 3 4
initially yields the factors 3 and 4; a second
reduction is needed to reduce 4 to 2 2. 23 34
Multiplying the shared prime factors then 2 2
yields the greatest common factor of the 3=6
two numbers. If the two numbers have only Find the greatest common factor.
one shared prime factor, that number is their
greatest common factor. 6= 2 3 2
12 = 2 2 3
1. Have students solve the problems
individually. The GCF: 6
1 . Find the greatest common factor using the method above.
a. 6 and 20 20 b. 12 and 42 42
6 12
2345 2676
22 232 3
6= 2 3 12 = 2 2 3
20 = 2 25 42 = 2 3 7
The GCF: 2 The GCF: 6
c. 25 and 40 5 d. 36 and 48 12
The GCF: The GCF:
12
2. Build Understanding
This reducing method relies on the fact that all factors of a number are either prime numbers or the product
of other numbers; in the latter case the factor can thus be reduced, or “broken down,” eventually reaching
prime numbers.
The prime factors of a number cannot be further broken down (except to the trivial cases of 1 and the
number itself). If two numbers have only one common prime factor, that prime factor is their greatest
common factor; if they have more than one, the prime factors multiplied yield the greatest common factor.
020 NUMINO Teacher s Guide
jOb ective Determine the greatest common factor of two numbers.
1. Textbook Instructions Activity 1 The Greatest Common Factor
This activity introduces more systematic and Go over these two methods of finding the GCF of two numbers.
efficient methods of determining the greatest Have students choose the method that is easier for them to follow.
common factor of two numbers.
Learn how to find the greatest common factor.
Method 1: Use prime factorization.
First, the method of prime factorization is Method 1 Use prime factorization.
introduced. The prime factors of a single
number are determined by progressively Find the greatest common factor of 6 and 12.
decomposing its factors.
Find the prime factorization of 6 and 12.
Example: 6 and 12.
6 at once yields the prime factors 2 and 3. 12 6=2 3 12 = 3 4
initially yields the factors 3 and 4; a second
reduction is needed to reduce 4 to 2 2. 23 34
Multiplying the shared prime factors then 2 2
yields the greatest common factor of the 3=6
two numbers. If the two numbers have only Find the greatest common factor.
one shared prime factor, that number is their
greatest common factor. 6= 2 3 2
12 = 2 2 3
1. Have students solve the problems
individually. The GCF: 6
1 . Find the greatest common factor using the method above.
a. 6 and 20 20 b. 12 and 42 42
6 12
2345 2676
22 232 3
6= 2 3 12 = 2 2 3
20 = 2 25 42 = 2 3 7
The GCF: 2 The GCF: 6
c. 25 and 40 5 d. 36 and 48 12
The GCF: The GCF:
12
2. Build Understanding
This reducing method relies on the fact that all factors of a number are either prime numbers or the product
of other numbers; in the latter case the factor can thus be reduced, or “broken down,” eventually reaching
prime numbers.
The prime factors of a number cannot be further broken down (except to the trivial cases of 1 and the
number itself). If two numbers have only one common prime factor, that prime factor is their greatest
common factor; if they have more than one, the prime factors multiplied yield the greatest common factor.
020 NUMINO Teacher s Guide
