Page 39 - NUMINO TG_6A
P. 39
Activity 2 The GCF of Three Numbers
jOb ective Determine the greatest common factor of three numbers.
1. Textbook Instructions Activity 2 The GCF of Three Numbers
This activity uses the greatest common Go over the method of finding the GCF of three numbers.
factors to determine the GCF of three
numbers (rather than two). Learn how to find the greatest common factor of three numbers.
Go through the sample, reverting to the
exhaustive (but sure) method of listing all the Find the greatest common factor of 12, 18, and 30.
factors of each number, sequenced from the Find the common factors of 12, 18, and 30.
smallest to the largest; then, determining the Factors of 12: 1, 2, 3, 4, 6, 12
greatest factor shared by all three in common. Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common factors of 12, 18, and 30: 1, 2, 3, 6
Find the largest number among the common factors.
The greatest common factor of 12, 18, and 30: 6
1. Have students solve the problems. The Have students apply the method learned to solve the following problems.
solutions will yield some non-obvious results.
1 . Find the greatest common factor of the three numbers.
1c. This problem involves relatively large even a. 12, 30, 42 b. 27, 45, 15
numbers that students might expect to share The GCF: 6 The GCF: 3
multiple common factors, but in fact their
greatest common factor is 2, because 14
yields prime factors 2 and 7, and 7 is not a c. 36, 14, 20 d. 39, 13, 26
The GCF: The GCF:
factor of either 36 or 20. 2 13
Are there simpler ways to solve these
problems?
Refer to . e. 10, 20, 30 f. 40, 56, 72
The GCF: The GCF:
10 8
14
2. Build Understanding
Working out all the factors of three numbers can be cumbersome. One simplifying approach is to use either
of the methods introduced previously, reduction into prime factors or the ladder diagram, on any two of the
target numbers. Then apply the same method to the resulting partial GCF and the third number.
Example: 36, 14, and 20
2 36 14 2 2 20 The GCF of the three numbers is 2.
18 7 1 10
GCF: 2 GCF: 2
022 NUMINO Teacher s Guide
jOb ective Determine the greatest common factor of three numbers.
1. Textbook Instructions Activity 2 The GCF of Three Numbers
This activity uses the greatest common Go over the method of finding the GCF of three numbers.
factors to determine the GCF of three
numbers (rather than two). Learn how to find the greatest common factor of three numbers.
Go through the sample, reverting to the
exhaustive (but sure) method of listing all the Find the greatest common factor of 12, 18, and 30.
factors of each number, sequenced from the Find the common factors of 12, 18, and 30.
smallest to the largest; then, determining the Factors of 12: 1, 2, 3, 4, 6, 12
greatest factor shared by all three in common. Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common factors of 12, 18, and 30: 1, 2, 3, 6
Find the largest number among the common factors.
The greatest common factor of 12, 18, and 30: 6
1. Have students solve the problems. The Have students apply the method learned to solve the following problems.
solutions will yield some non-obvious results.
1 . Find the greatest common factor of the three numbers.
1c. This problem involves relatively large even a. 12, 30, 42 b. 27, 45, 15
numbers that students might expect to share The GCF: 6 The GCF: 3
multiple common factors, but in fact their
greatest common factor is 2, because 14
yields prime factors 2 and 7, and 7 is not a c. 36, 14, 20 d. 39, 13, 26
The GCF: The GCF:
factor of either 36 or 20. 2 13
Are there simpler ways to solve these
problems?
Refer to . e. 10, 20, 30 f. 40, 56, 72
The GCF: The GCF:
10 8
14
2. Build Understanding
Working out all the factors of three numbers can be cumbersome. One simplifying approach is to use either
of the methods introduced previously, reduction into prime factors or the ladder diagram, on any two of the
target numbers. Then apply the same method to the resulting partial GCF and the third number.
Example: 36, 14, and 20
2 36 14 2 2 20 The GCF of the three numbers is 2.
18 7 1 10
GCF: 2 GCF: 2
022 NUMINO Teacher s Guide
