4. Arnel helps his father in their bakeshop.
They bake 48 cupcakes and 60 cookies.
They plan to pack them separately in
small boxes. What is the biggest
number of cupcakes and cookies that
can be placed in boxes if these are the
same number?
• What did Arnel and his father bake?
• How many cupcakes were baked?
• How many cookies were baked?
• What do Arnel and his father plan to do with the
cupcakes and cookies?
• How will you solve for the answer to the problem?
5. Solution 1: Finding the Common
Factors and Greatest
Common Factor (GCF) by
listing the factors of 48 and 60.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12,
1, 24, and 48.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10,
12, 15, 20, 30 and 60.
Common Factors: 1, 2, 3, 4, 6 and 12
Greatest Common Factor: 12
6. Solution 2: Finding the Greatest Common Factor
(GCF) of 48 and 60 by prime factorization.
48
2 × 24
2 × 12
3 × 4
2 × 2
60
2 × 30
2 × 15
3 × 5
48 = 2 × 2 × 2 ×
2 × 3
60 = 2 × 2 × 3 ×
5
Common Prime
Factors: 2 × 2
× 3
Greatest Common
Factor or GCF:
12
7. Solution 3 Finding the GCF of 48
and 60 by continuous division.
2 48 60
2 24 30
3 12 15
4 5
8. Alvin has 12 guavas and
Elorde has 18 guavas. Each
of them will share the guavas
to their friends. What is the
greatest number of guavas
each of their friends get if
Alvin and Elorde will give the
same number of guavas?
9. Method 1:
By listing the factors of 12 and 18.
Factors of 12: 1, 2, 3, 4, 6, and 12
Factors of 18: 1, 2, 3, 6, 9, and 18
By finding the common factors of 12 and 18
Common factors of 12 and 18: 1, 2, 3, and 6
By getting the Greatest common Factor (GCF) of
12 and 18
The GCF of 12 and 18 is 6.
10. GCF: 2 × 3 = 6
Method 2: By writing each number
as a product of its prime factors.
12
2 × 6
2 × 3
12 = 2 ×
2 × 3
18
2 × 9
3 × 3
18 = 2 ×
3 × 3
2 12 18
3 6 9
2 3
11. By multiplying the common prime
factors of 12 and 18.
GCF = 2 × 3 = 6 So, each of their friends
gets 6 guavas
1
2
= 2 × 2 × 3
1
8
= 2 × 3 × 3
12. List the factors of each number below.
a) 16 b) 24 c) 30 d) 36 e) 54
Write each number as a product of its prime
factors using factor tree.
a) 12 b) 18 c) 24 d) 16 e) 30
Find the Greatest Common Factor of the following
pairs of numbers using the following methods:
Listing, Prime Factorization, and Continuous Division.
a) 12 and 16 b) 18 and 24 c) 20 and 30 d) 36 and 54
13. A. Write each number as a product of its
prime factors. Use factor thee. The first
one is done for you.
1. 16 16
2 × 8
2 × 4
2 × 2
16 = 2× 2 × 2 × 2
2. 24 3. 30
4. 32 5. 48
24 = _______________
30 = _______________
32 = _______________
48 = _______________
14. B. List all the factors of each number. Then, find
the common factors and the greatest
common factor of each pair of number.
1. 18 =
_________________________________
27 =
_________________________________
Common factors:
______________________
GCF:
________________________________
2. 21 =
_________________________________
17. B. Find the GCF of each pair of numbers. Use listing
method, prime factorization, and continuous
division. Write your answers in your notebook.
1) 15 and 20 6) 12 and 8
2) 16 and 20 7) 5 and 6
3) 9 and 21 8) 9 and 27
4) 17 and 51 9) 21 and 30
5) 36 and 42 10) 16 and 56
18. What is prime
factorization?
Prime factorization is the
process of writing a number as
a product of its prime factors.
What are common
factors?
Common factors are factors
common to two numbers.
What is Greatest
Common Factor or
GCF of two numbers?
Greatest Common Factor
or GCF is the biggest factor
common to two numbers.
How do we find the
Greatest Common
Factor (GCF) of two
given numbers?
We find the Greatest Common Factor
(GCF) of 2 numbers by listing method,
prime factorization, and continuous
division.
19. • Write the numbers horizontally and find a
prime number that will divide the numbers, if
possible.
• Divide by that prime number and write the
quotients below the dividends. Copy any
numbers not divided by them.
• Continue the process until no two numbers
have a common prime divisor.
• Multiply all the prime divisors common to the
given numbers to get the GCF.
20. 1. Ian and Isagani went fishing. Ian caught
21 fish and Isagani caught 28 fish. What
is the greatest number of fish each could
catch per hour, if they caught the same
number of fish per hour?
2. Mr. Rojas has 2 pieces of wood for his
scrabble board. One had a width f 18 cm
and the other one has 20 cm. if both sizes
of wood are to be cut into scrabble tiles of
the same width without wasting any wood,
21. Read the problem and then write the
answers to the questions in your
notebook.
Aling Juanita has 100 pieces of suman to sell.
She wants to sell them in pairs, fours, fives, and
tens.
a. How will Aling Juanita sell the pieces of suman
given her plan?
b. Can Aling Juanita sell all the pieces of suman if
she sells them in threes, sixes, and by the dozen?
How?
22. Do the following activities. Write the answers on
your answer sheet. Write each number as a
product of its prime factors using the factor
tree.
1) 28 5) 64
2) 40 6) 72
3) 42 7) 81
4) 27 8) 100
23. Find the Greatest Common factor (GCF) of
the given number pairs by listing
method, prime factorization, and
continuous division.
1) 16 and 24 5) 18 and 27
2) 20 and 30 6) 36 and 45
3) 21 and 35 7) 48 and 56
4) 32 and 40 8) 63 and 72
24. Provide the following exercises. You may give
more. Write each number as a product of its
prime factors.
1) 12 2) 14 3) 20
4) 27 5) 33 6) 48
Provide the following exercises. You may give
more. Write each number as a product of its
prime factors.
7) 15 and 18 9) 16 and 32
8) 20 and 28 10) 18 and 30
25. Ask the pupils to answer the
following questions.
1. What is the Greatest Common Factor
of 2 × 2 × 3 × 5 and 2 × 3 × 3 × 5?
2. What is the Greatest Common Factor
of 2 × 3 × 5 × 7 and 2 × 2 × 3 × 5
× 7?
3. What is the GCF of 120 and 160?
