Page 36 - NUMINO TG_6A
P. 36
02Which Is the Greatest? Unit
CMath Vo abulary common factor: a number that is a factor of two or more numbers
greatest common factor: the largest common factor of two or more numbers
Objective: Learn how to find common factors and the greatest common factor The greatest common factor is now
introduced, along with a full approach to
Learn about the greatest common factor. determining the greatest common factor of
two numbers:
The greatest common factor(GCF) is the largest common factor Line 1: factors of the first number
of two or more numbers. Line 2: factors of the second number
Line 3: common factors of the two numbers
Find the factors and common factors of the two numbers. Then find Line 4: the greatest common factor.
the greatest common factor.
Example: 6 and 28.
6 and 28 Factors of 6: 1, 2, 3, 6 6 and 28 have only two common factors, 1
Factors of 28: 1, 2, 4, 7, 14, 28 and 2, so 2 is the greatest common factor.
Common factors: 1, 2 2
Have students solve the problems. Some
The greatest common factor: students may quickly grasp that because 14
goes evenly into 28, it is also the greatest
14 and 28 14 common factor.
Factors of 14: 1, 2, 7, 14 The third exercise challenges students to
Factors of 28: 1, 2, 4, 7, 14, 28 solve the problem for an even number and a
Common factors: 1, 2, 7, 14 relatively large odd number, which share few
The greatest common factor: common factors.
18 and 45 9
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 45: 1, 3, 5, 9, 15, 45
Common factors: 1, 3, 9
The greatest common factor:
2. Which Is the Greatest? 11
If both numbers are even, 2 is always a common factor, while if either number is odd, 2 is ruled out as a
common factor. Invite students to think about what “even” and “odd” imply about numbers (i.e., divisibility
by 2).
If, of two numbers, one is a multiple of the other, the smaller of the two numbers is their greatest common
factor, and no further work is required to determine this value.
The corollary to this insight is that if the larger number is not a multiple of the smaller, the smaller number
will not be a common factor of the two.
6A Unit 02 019
CMath Vo abulary common factor: a number that is a factor of two or more numbers
greatest common factor: the largest common factor of two or more numbers
Objective: Learn how to find common factors and the greatest common factor The greatest common factor is now
introduced, along with a full approach to
Learn about the greatest common factor. determining the greatest common factor of
two numbers:
The greatest common factor(GCF) is the largest common factor Line 1: factors of the first number
of two or more numbers. Line 2: factors of the second number
Line 3: common factors of the two numbers
Find the factors and common factors of the two numbers. Then find Line 4: the greatest common factor.
the greatest common factor.
Example: 6 and 28.
6 and 28 Factors of 6: 1, 2, 3, 6 6 and 28 have only two common factors, 1
Factors of 28: 1, 2, 4, 7, 14, 28 and 2, so 2 is the greatest common factor.
Common factors: 1, 2 2
Have students solve the problems. Some
The greatest common factor: students may quickly grasp that because 14
goes evenly into 28, it is also the greatest
14 and 28 14 common factor.
Factors of 14: 1, 2, 7, 14 The third exercise challenges students to
Factors of 28: 1, 2, 4, 7, 14, 28 solve the problem for an even number and a
Common factors: 1, 2, 7, 14 relatively large odd number, which share few
The greatest common factor: common factors.
18 and 45 9
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 45: 1, 3, 5, 9, 15, 45
Common factors: 1, 3, 9
The greatest common factor:
2. Which Is the Greatest? 11
If both numbers are even, 2 is always a common factor, while if either number is odd, 2 is ruled out as a
common factor. Invite students to think about what “even” and “odd” imply about numbers (i.e., divisibility
by 2).
If, of two numbers, one is a multiple of the other, the smaller of the two numbers is their greatest common
factor, and no further work is required to determine this value.
The corollary to this insight is that if the larger number is not a multiple of the smaller, the smaller number
will not be a common factor of the two.
6A Unit 02 019
