Page 38 - NUMINO TG_6A
P. 38
02Which Is the Greatest? Unit
Method 2 Use a ladder diagram. Method 2: Use a ladder diagram.
Find the greatest common factor of 12 and 24. Introduce an alternative approach to
determining the greatest common factor by
Use a ladder diagram to divide the numbers using common factors. the use of a ladder diagram.
A common factor of 12 and 24 4 12 24 In this method we first choose some
common factor (avoiding the trivial 1), and
A common factor of 3 and 6 33 6 determine how many times that common
factor goes into each number. This provides
12 us with a new pair of numbers, written
below the first pair.
Find the greatest common factor.
A common factor is then found for those
4 12 24 4 3 = 12 two numbers, the process continuing until
33 6 no further (non-trivial) steps are possible.
The common factors on the left can then be
12 multiplied to yield the greatest common
The GCF: 12 factor.
2 . Find the greatest common factor using the method above.
a . 2 12 30 b . 2 20 30
3 6 15 5 10 15
25 23
The GCF: 2 3 = 6 The GCF: 2 5 = 10 2. Have students solve the problems. Have
c . 6 36 18 d . 5 45 75 students discuss which method they think is
36 3 3 9 15 easier, and why.
21 35
Refer to .
The GCF: 6 3 = 18 The GCF: 5 3 = 15
2. Which Is the Greatest? 13
There is no “right” answer as to which of these methods is better. Both are valid, producing the greatest
common factor if employed correctly. The choice is a matter of preference, or possibly learning style.
Many students will find the ladder diagram to be faster and easier to work, but other students may find it
confusing because it seems to rely on an element of guesswork, arbitrarily picking a common factor.
In fact the ladder diagram works because whatever (non-trivial) common factor we start with, the end result
is a reduction into prime factors.
6A Unit 02 021
Method 2 Use a ladder diagram. Method 2: Use a ladder diagram.
Find the greatest common factor of 12 and 24. Introduce an alternative approach to
determining the greatest common factor by
Use a ladder diagram to divide the numbers using common factors. the use of a ladder diagram.
A common factor of 12 and 24 4 12 24 In this method we first choose some
common factor (avoiding the trivial 1), and
A common factor of 3 and 6 33 6 determine how many times that common
factor goes into each number. This provides
12 us with a new pair of numbers, written
below the first pair.
Find the greatest common factor.
A common factor is then found for those
4 12 24 4 3 = 12 two numbers, the process continuing until
33 6 no further (non-trivial) steps are possible.
The common factors on the left can then be
12 multiplied to yield the greatest common
The GCF: 12 factor.
2 . Find the greatest common factor using the method above.
a . 2 12 30 b . 2 20 30
3 6 15 5 10 15
25 23
The GCF: 2 3 = 6 The GCF: 2 5 = 10 2. Have students solve the problems. Have
c . 6 36 18 d . 5 45 75 students discuss which method they think is
36 3 3 9 15 easier, and why.
21 35
Refer to .
The GCF: 6 3 = 18 The GCF: 5 3 = 15
2. Which Is the Greatest? 13
There is no “right” answer as to which of these methods is better. Both are valid, producing the greatest
common factor if employed correctly. The choice is a matter of preference, or possibly learning style.
Many students will find the ladder diagram to be faster and easier to work, but other students may find it
confusing because it seems to rely on an element of guesswork, arbitrarily picking a common factor.
In fact the ladder diagram works because whatever (non-trivial) common factor we start with, the end result
is a reduction into prime factors.
6A Unit 02 021
