HCF Adventure for Class 4 Students!

List all factors of each number, find the common ones, and pick the largest.

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18

Common factors: 1, 2, 3, 6
HCF is: 6

Break down each number into its prime factors. The HCF is the product of all common prime factors.

2	16
2	8
2	4
2	2
	1

2	24
2	12
2	6
3	3
	1

2	40
2	20
2	10
5	5
	1

How the Prime Factorization Table Works

We have seen 3 tables above that were created in this method. Let me clarify how these tables were created. For example, we will discuss the table of ’40’ above:

2	40
2	20
2	10
5	5
	1

Goal: Find the “Secret Code” of 40

The goal is to find which prime numbers multiply together to make 40.

The Step-by-Step Ladder Method 🪜

The table is like a ladder that we climb down, dividing as we go.

Step 1: Start at the Top

We begin with our number, 40, at the top right. We ask, “What is the smallest prime number that can divide 40 evenly?” The answer is 2.

We write the divisor (2) on the left.

We do the math: 40 ÷ 2 = 20. We write the result (20) below 40.

Step 2: Climb Down to the Next Rung

Now we focus on the new number, 20. What’s the smallest prime number that divides 20? It’s 2 again.

We write the divisor (2) on the left.

We do the math: 20 ÷ 2 = 10. We write the result (10) below 20.

Step 3: Keep Going!

Our new number is 10. The smallest prime that divides 10 is also 2.

We write the divisor (2) on the left.

We do the math: 10 ÷ 2 = 5. We write the result (5) below 10.

Step 4: Almost There!

Now we have 5. The smallest prime that divides 5 is 5 itself.

We write the divisor (5) on the left.

We do the math: 5 ÷ 5 = 1. We write the final result (1) at the bottom.

The Final Answer

Once you reach 1, you’re done!

The prime factors of 40 are all the numbers you wrote in the left column. So, the prime factorization of 40 is 2, 2, 2, and 5.

It works! You’ve found the secret prime code for the number 40.

Accordingly, from the above tables, we have found the following:

16 = 2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
40 = 2 × 2 × 2 × 5

Common prime factors are: 2, 2, 2
HCF = 2 × 2 × 2 = 8

Divide the larger number by the smaller one. Then divide the previous divisor by the remainder. The last non-zero remainder is the HCF.

24: 1, 2, 3, 4, 6, 8, 12, 24;
36: 1, 2, 3, 4, 6, 9, 12, 18, 36;
60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Common: 1, 2, 3, 4, 6, 12
HCF: 12

2	24
2	12
2	6
3	3
	1

2	36
2	18
3	9
3	3
	1

2	60
2	30
3	15
5	5
	1

24 = 2 × 2 × 2 × 3,
36 = 2 × 2 × 3 × 3,
60 = 2 × 2 × 3 × 5

Common Prime Factors: 2, 2, 3
Therefore, HCF: 2 × 2 × 3 = 12

60 ÷ 36 = 1, remainder 24;
36 ÷ 24 = 1, remainder 12;
24 ÷ 12 = 2, remainder 0

HCF: 12

16: 1, 2, 4, 8, 16;
24: 1, 2, 3, 4, 6, 8, 12, 24;
40: 1, 2, 4, 5, 8, 10, 20, 40

Common: 1, 2, 4, 8
HCF: 8

2	16
2	8
2	4
2	2
	1

2	24
2	12
2	6
3	3
	1

2	40
2	20
2	10
5	5
	1

16 = 2 × 2 × 2 × 2,
24 = 2 × 2 × 2 × 3,
40 = 2 × 2 × 2 × 5

Common Prime Factors: 2, 2, 2
Therefore, HCF: 2 × 2 × 2 = 8

40 ÷ 24 = 1, remainder 16;
24 ÷ 16 = 1, remainder 8;
16 ÷ 8 = 2, remainder 0

HCF: 8

4: 1, 2, 4;
6: 1, 2, 3, 6

Common: 1, 2
HCF: 2

2	4
2	2
	1

2	6
3	3
	1

4 = 2 × 2,
6 = 2 × 3

Common Prime Factors: 2
Therefore, HCF: 2

6 ÷ 4 = 1, remainder 2;
4 ÷ 2 = 2, remainder 0

HCF: 2

12: 1, 2, 3, 4, 6, 12;
32: 1, 2, 4, 8, 16, 32;
36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Common: 1, 2, 4
HCF: 4

2	12
2	6
3	3
	1

2	32
2	16
2	8
2	4
2	2
	1

2	36
2	18
3	9
3	3
	1

12 = 2 × 2 × 3,
32 = 2 × 2 × 2 × 2 × 2,
36 = 2 × 2 × 3 × 3

Common Prime Factors: 2, 2
Therefore, HCF: 2 × 2 = 4

36 ÷ 32 = 1, remainder 4;
32 ÷ 12 = 2, remainder 8;
12 ÷ 4 = 3, remainder 0

HCF: 4

16: 1, 2, 4, 8, 16;
24: 1, 2, 3, 4, 6, 8, 12, 24

Common: 1, 2, 4, 8
HCF: 8

2	16
2	8
2	4
2	2
	1

2	24
2	12
2	6
3	3
	1

16 = 2 × 2 × 2 × 2,
24 = 2 × 2 × 2 × 3

Common Prime Factors: 2, 2, 2
Therefore, HCF: 2 × 2 × 2 = 8

24 ÷ 16 = 1, remainder 8;
16 ÷ 8 = 2, remainder 0

HCF: 8

18: 1, 2, 3, 6, 9, 18;
27: 1, 3, 9, 27

Common: 1, 3, 9
HCF: 9

2	18
3	9
3	3
	1

3	27
3	9
3	3
	1

18 = 2 × 3 × 3,
27 = 3 × 3 × 3

Common Prime Factors: 3, 3
Therefore, HCF: 3 × 3 = 9

27 ÷ 18 = 1, remainder 9;
18 ÷ 9 = 2, remainder 0

HCF: 9

6: 1, 2, 3, 6;
9: 1, 3, 9

Common: 1, 3
HCF: 3

2	6
3	3
	1

3	9
3	3
	1

6 = 2 × 3,
9 = 3 × 3

Common Prime Factors: 3
Therefore, HCF: 3

9 ÷ 6 = 1, remainder 3;
6 ÷ 3 = 2, remainder 0

HCF: 3

35: 1, 5, 7, 35;
49: 1, 7, 49

Common: 1, 7
HCF: 7

5	35
7	7
	1

7	49
7	7
	1

35 = 5 × 7,
49 = 7 × 7

Common Prime Factors: 7
Therefore, HCF: 7

49 ÷ 35 = 1, remainder 14;
35 ÷ 14 = 2, remainder 7;
14 ÷ 7 = 2, remainder 0

HCF: 7

36: 1, 2, 3, 4, 6, 9, 12, 18, 36;
18: 1, 2, 3, 6, 9, 18

Common: 1, 2, 3, 6, 9, 18
HCF: 18

2	36
2	18
3	9
3	3
	1

2	18
3	9
3	3
	1

36 = 2 × 2 × 3 × 3,
18 = 2 × 3 × 3

Common Prime Factors: 2, 3, 3
Therefore, HCF: 2 × 3 × 3 = 18

36 ÷ 18 = 2, remainder 0

HCF: 18

42: 1, 2, 3, 6, 7, 14, 21, 42;
112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

Common: 1, 2, 7, 14
HCF: 14

2	42
3	21
7	7
	1

2	112
2	56
2	28
2	14
7	7
	1

42 = 2 × 3 × 7,
112 = 2 × 2 × 2 × 2 × 7

Common Prime Factors: 2, 7
Therefore, HCF: 2 × 7 = 14

112 ÷ 42 = 2, remainder 28;
42 ÷ 28 = 1, remainder 14;
28 ÷ 14 = 2, remainder 0

HCF: 14

14: 1, 2, 7, 14;
21: 1, 3, 7, 21;
28: 1, 2, 4, 7, 14, 28

Common: 1, 7
HCF: 7

2	14
7	7
	1

3	21
7	7
	1

2	28
2	14
7	7
	1

14 = 2 × 7,
21 = 3 × 7,
28 = 2 × 2 × 7

Common Prime Factors: 7
Therefore, HCF: 7

28 ÷ 21 = 1, remainder 7;
21 ÷ 14 = 1, remainder 7;
14 ÷ 7 = 2, remainder 0

HCF: 7

5: 1, 5;
15: 1, 3, 5, 15;
25: 1, 5, 25

Common: 1, 5
HCF: 5

5	5
	1

3	15
5	5
	1

5	25
5	5
	1

5 = 5,
15 = 3 × 5,
25 = 5 × 5

Common Prime Factors: 5
Therefore, HCF: 5

25 ÷ 15 = 1, remainder 10;
15 ÷ 5 = 3, remainder 0

HCF: 5