The document describes the ladder method for finding the greatest common factor (GCF) of two or more numbers using continuous division. It involves writing the numbers horizontally, dividing them by common prime factors until no two numbers share a factor, and multiplying the shared factors to get the GCF. Several examples are provided of using this method to find the GCF of pairs, triples and quadruples of numbers.

1. How do we find the Greatest
Common Factor (GCF) of two
given numbers using
continuous division? Or the
Ladder Method
Prepared by:
Teacher Michelle Rose Naynes

2. Continuous division is done
following the steps below:

3. Step 1:
Write the number horizontally

4. Step 2:
Find a prime number that will
divide the numbers, if possible.

5. Step 3:
Divide the given numbers by that
prime number and write the
quotients below.

6. Step 4:
Continue the process until no two
numbers have a common prime
divisor.

7. Step 5:
Multiply all the prime divisors
common to the given numbers to
get the GCF.

8. Finding the GCF of
4 Numbers

9. Red Group
36, 60, 84 and 108

10. Green Group
12, 16, 24 and 36

11. Yellow Group
48, 56, 64 and 72

12. Orange Group
27, 45, 63, and 81

13. Red Group
36, 60, 84 and 108
36, 60, 84 , 108
2
18, 30, 42 , 54
2
9, 15, 24 , 27
3
3, 5 , 6 , 9
2 x 2 x 3 = 12

14. Green Group
12, 16, 24 and 36
12, 16, 24 , 36
2
6, 8 , 12 , 18
2
3 , 4 , 6 , 9
2 x 2 = 4

15. Yellow Group
48, 56, 64 and 72
48, 56, 64 , 72
2
24, 28, 32 , 36
2
6, 14, 16 , 18
2
3, 7 , 8 , 9
2 x 2 x 2 = 8

16. Orange Group
27, 45, 63 and 81
27, 45, 63 , 81
3
9, 15, 21 , 27
3
3, 5, 7 , 9
3 x 3= 9

17. Easiest Way to get GCF.
HOW?

18. Think of the Biggest
Number that can divide the
given Numbers.
And that will be your GCF

19. Example
18 and 27
GCF = 9

20. 24 and 12
GCF = 12

21. 16 and 20
GCF = 4

22. Do it Mentally

23. 32 and 24
GCF = 8

24. 20 and 10
GCF = 10

25. 45 and 10
GCF = 5

26. 12 and 18
GCF = 6

27. 100 and 50
GCF = 50

28. 40 and 20
GCF = 20

29. 15 and 18
GCF = 3

30. 36 and 48
GCF = 6

31. 54 and 72
GCF = 9

32. For 3 numbers
18 , 27 , 30
GCF = 3

33. 24 , 36 , 40
GCF = 4

34. 75 , 15 , 30
GCF = 15

35. 32 , 16 , 56
GCF = 8

36. For 4 numbers
24, 40, 36, 12
GCF = 4

37. 25, 35, 20, 15
GCF = 5

38. 150, 50, 100, 75
GCF = 25

39. 36 , 24 , 60, 72
GCF = 12

40. Find the GCF of the following
problems using continuous
division.

41. Miss Dela Cueva has to prepare number of exercises
for her lesson for the day. She has three classes. One
class has 48 pupils, another class has 50, and another
has 46. What must be the largest number of exercises
she should prepare so that each class will have the
same number of pupils working on different
problems?

42. 48, 50, 56
2
24, 25, 28
Answer: 2

43. There are 10 green, 14 blue, 20 red and 24 yellow
bulbs to be used for a birthday party. They are to be
placed in plastic bags so that each bag contains the
same number of green, blue, red and yellow bulbs.
What is the largest number of plastic bags that will be
needed?

44. 10, 14, 20, 24
2
5, 7, 10, 12
GCF: 4
2

45. A group of 45 dancers will march behind a group of
30 clowns in a parade. You want to arrange the two
groups in rows with the same number of people in
each row, but without mixing the group. What is the
greatest number of people you can have in each
row?

46. 45, 30
5
9, 6
GCF: 15
3
3, 2

47. The parents are making sandwiches for the class
picnic. They have 72 ham slices, 48 cheese slices, and
96 tomato slices. What is the greatest number of
sandwiches they can make if each sandwich has the
same filling?

48. 72, 48, 96
2
36, 24, 32
GCF: 6
2
18, 12, 16
2
9, 6, 8

49. Assessment
1.) 30, 75, 120, 150
2.)90, 135, 180, 195
3.)42, 56, 70, 98

50. 30, 75, 120, 150
5
15, 15, 24, 30
GCF: 15
3
5, 5, 8, 10

51. 90, 135, 180, 195
5
18, 27, 36, 39
GCF: 15
3
6, 9, 12, 13

52. 42, 56, 70, 98
2
21, 28, 35, 49
GCF: 14
7
3, 4, 5, 7