Page 40 - NUMINO TG_6A
P. 40
02Which Is the Greatest? Unit
Have students figure out the problems below and recognize where they can use the GCF. 2. Have students work in groups to solve the
word problems.
2 . Solve the word problems.
2a. This problem: Ann must pack boxes with
a. Ann has 16 donuts and 28 cartons of milk. She wants to pack an equal donuts and milk cartons; each box having the
number of donuts and cartons of milk in each box with none left over. What same quantities. The GCF is 4, thus she can
is the greatest number of boxes she can pack? pack four boxes (each having four donuts and
seven cartons of milk).
4 16 28 4 boxes
47 2b. This problem: dividing a 35 25 rectangle
into squares, the GCF is 5, thus 5 5 squares
The GCF of 16 and 28 is 4. are the largest that can be evenly cut out of it
(and there will be 35 such squares).
b. You want to cut a rectangle that is 25 cm wide and 35 cm long into squares
of equal sizes. If you do not want any area of the rectangle left over, what is 2c. This problem requires determining the
the length of the largest square that you can make? GCF of three numbers. Working out how
many items each player gets may be
5 25 35 5 cm instructive, though not strictly necessary to
57 mastering the problem.
The GCF of 25 and 35 is 5.
c. A soccer team coach needs to give out an equal number of uniforms,
shoes, and soccer balls with none left over. If the coach has
12 uniforms, 36 pairs of shoes, and 16 soccer balls, what is the greatest
number of players he can give them out to?
Factors of 12: 1, 2, 3, 4, 6, 12 4 players
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 16: 1, 2, 4, 8, 16
The GCF of 12, 36, and 16 is 4.
2. Which Is the Greatest? 15
Any time we want to divide some quantity “with none left over,” we are looking for the factors of that
quantity. Thus, in the first problem, Ann’s 16 donuts could be evenly divided into two groups of eight each,
four groups of four each, or eight groups of two each. These turn out to be the factors of 16 (as well as the
trivial 1 and 16).
Thus, the word problem’s requirement to divide two or more quantities evenly is a tipoff that the problem
involves common factors, and the greatest possible number of such divisions will be the greatest common
factor.
6A Unit 02 023
Have students figure out the problems below and recognize where they can use the GCF. 2. Have students work in groups to solve the
word problems.
2 . Solve the word problems.
2a. This problem: Ann must pack boxes with
a. Ann has 16 donuts and 28 cartons of milk. She wants to pack an equal donuts and milk cartons; each box having the
number of donuts and cartons of milk in each box with none left over. What same quantities. The GCF is 4, thus she can
is the greatest number of boxes she can pack? pack four boxes (each having four donuts and
seven cartons of milk).
4 16 28 4 boxes
47 2b. This problem: dividing a 35 25 rectangle
into squares, the GCF is 5, thus 5 5 squares
The GCF of 16 and 28 is 4. are the largest that can be evenly cut out of it
(and there will be 35 such squares).
b. You want to cut a rectangle that is 25 cm wide and 35 cm long into squares
of equal sizes. If you do not want any area of the rectangle left over, what is 2c. This problem requires determining the
the length of the largest square that you can make? GCF of three numbers. Working out how
many items each player gets may be
5 25 35 5 cm instructive, though not strictly necessary to
57 mastering the problem.
The GCF of 25 and 35 is 5.
c. A soccer team coach needs to give out an equal number of uniforms,
shoes, and soccer balls with none left over. If the coach has
12 uniforms, 36 pairs of shoes, and 16 soccer balls, what is the greatest
number of players he can give them out to?
Factors of 12: 1, 2, 3, 4, 6, 12 4 players
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 16: 1, 2, 4, 8, 16
The GCF of 12, 36, and 16 is 4.
2. Which Is the Greatest? 15
Any time we want to divide some quantity “with none left over,” we are looking for the factors of that
quantity. Thus, in the first problem, Ann’s 16 donuts could be evenly divided into two groups of eight each,
four groups of four each, or eight groups of two each. These turn out to be the factors of 16 (as well as the
trivial 1 and 16).
Thus, the word problem’s requirement to divide two or more quantities evenly is a tipoff that the problem
involves common factors, and the greatest possible number of such divisions will be the greatest common
factor.
6A Unit 02 023
