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LCM
Two Numbers Three Numbers Multiple Numbers Prime Factorization Division Listing Multiples Ladder Exponents Venn Diagram Factor Tree
HCF
Two Numbers Three Numbers Multiple Numbers Prime Factorization Listing Ladder Exponents Venn Diagram Division Factor Tree All Factors By Division All Factors By Multiplication

HCF of Multiple Numbers By Prime Factorization Using Ladder

Multiple Numbers Two Numbers Three Numbers
Method
Prime Factorization
Listing
Ladder
Exponents
Division
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Answer: HCF of 18, 24, 54, 60 is 6

Step A: Find the Factors Using Ladder

Factor Methods
Factors of 18
18
/ 2
9
/ 3
3
/ 3
1
Factors of 24
24
/ 2
12
/ 2
6
/ 2
3
/ 3
1
Factors of 54
54
/ 2
27
/ 3
9
/ 3
3
/ 3
1
Factors of 60
60
/ 2
30
/ 2
15
/ 3
5
/ 5
1

Ladder Help

1. Start with smallest prime factor.
2. Divide the number by it.
3. Write prime factor on right.
4. Place the quotient below.
5. Repeat with same prime factor.
6. Move to next prime factor if not divisible.
7. Continue until 1.
8. Numbers on the right are prime factors.

What is Ladder?

The ladder method involves repeatedly dividing the number by the smallest prime numbers, starting from 2 until the quotient becomes 1. The divisors are arranged in a ladder formation, hence the method name is ladder.

Step B: Find the HCF Using Prime Factorization

HCF Method
Calculate HCF
18
=
2
×
3
×
3
24
=
2
×
2
×
2
×
3
54
=
2
×
3
×
3
×
3
60
=
2
×
2
×
3
×
5
HCF
=
2
x
3
=
6

Prime Factorization Help

1. List the prime factors of numbers
2. Select common prime factors.
3. Multiply selected prime factors.
4. This gives the HCF.

What is Prime Factorization?

The prime factorization method is an effective approach to find the highest common factor or HCF of two or more numbers. The HCF represents the largest number that divides each given number without leaving any remainder.

Solved Examples

Examples

Example 1: Find the HCF of 15 and 20.
Solution:
Prime factorization of 15: 15 = 3, 5
Prime factorization of 20: 20 = 2, 2, 5
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(15, 20) = 5. Example 2: Find the HCF of 18 and 24.
Solution:
Prime factorization of 18: 18 = 2, 3, 3
Prime factorization of 24: 24 = 2, 2, 2, 3
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(18, 24) = 6. Example 3: Find the HCF of 8 and 12.
Solution:
Prime factorization of 8: 8 = 2, 2, 2
Prime factorization of 12: 12 = 2, 2, 3
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(8, 12) = 4.

Exercise

1. HCF(3,9,18) = 3
 2. HCF(50,70,90) = 10
 3. HCF(63,84,105) = 21
 4. HCF(15,25,35) = 5
 5. HCF(16,24,32) = 8
 6. HCF(5,10,15) = 5
 7. HCF(9,12,15) = 3
 8. HCF(6,9,15,18) = 3
 9. HCF(20,60,80) = 20
 10. HCF(20,35,40,50) = 5

Highest Common Factor (HCF)

What is HCF?

HCF is also known as Highest Common Factor, GCF or GCD. HCF is the largest number that divides each of the given numbers without leaving a remainder.
The HCF formula can be expressed as,
HCF Formula:
HCF = (a × b)/ LCM(a,b)
where, a and b = Two terms
LCM(a, b) = Least common multiple of a and b

How to find HCF?

The Highest common factor or HCF can be found using various methods, such as: Prime Factorization MethodDivision MethodListing MethodLadder MethodExponents MethodVenn Diagram Method

FAQ

What are the steps involved to find HCF?
1. Write down the given numbers.
2. Use the ladder method to find the prime factors of each number.
3. Identify the common prime factors.
4. Multiply these factors to find the HCF.
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