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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 Three Numbers By Venn Diagram Using Ladder

Three Numbers Two Numbers Multiple Numbers
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Prime Factorization
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Ladder
Exponents
Division
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Answer: HCF of 12, 18, 24 is 6

Step A: Find the Factors Using Ladder

Factor Methods
Factors of 12
12
/ 2
6
/ 2
3
/ 3
1
Factors of 18
18
/ 2
9
/ 3
3
/ 3
1
Factors of 24
24
/ 2
12
/ 2
6
/ 2
3
/ 3
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 Venn Diagram

HCF Method
Calculate HCF
3
2
2
2
3

Venn Diagram Help

1. Draw circles for numbers.
2. Circle represents the factors.
3. Place common factors in overlaps.
4. Keep unique factors separate.
5. Multiply overlapping factors.
6. Obtain the HCF.

What is Venn Diagram?

The Venn Diagram Method for HCF uses circles to represent prime factors of numbers. Common factors go in overlaps, unique factors in sections. Multiply within overlaps to get HCF quickly.

Solved Examples

Examples

Example 1: Find the HCF of 27, 36 and 45.
Solution:
Prime factors of 27 = 3, 3, 3
Prime factors of 36 = 2, 2, 3, 3
Multiply factors present in the common region of venn diagram to find the HCF.
Factors present in common region = 3, 3.
Therefore, HCF(27, 36, 45) = 9. Example 2: Find the HCF of 50, 75 and 100.
Solution:
Prime factors of 50 = 2, 5, 5
Prime factors of 75 = 3, 5, 5
Multiply factors present in the common region of venn diagram to find the HCF.
Factors present in common region = 5, 5.
Therefore, HCF(50, 75, 100) = 25. Example 3: Find the HCF of 72, 96 and 120.
Solution:
Prime factors of 72 = 2, 2, 2, 3, 3
Prime factors of 96 = 2, 2, 2, 2, 2, 3
Multiply factors present in the common region of venn diagram to find the HCF.
Factors present in common region = 2, 2, 2, 3.
Therefore, HCF(72, 96, 120) = 24.

Exercise

1. HCF(42,56,70) = 14
 2. HCF(18,27,36) = 9
 3. HCF(80,120,160) = 40
 4. HCF(16, 24, 32) = 8
 5. HCF(81, 108, 135) = 27
 6. HCF(60, 80, 100) = 20
 7. HCF(48, 64, 80) = 16
 8. HCF(18, 24, 30) = 6
 9. HCF(42, 56, 70) = 14
 10. HCF(88, 110, 132) = 44

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. List the factors of each number.
2. Create a Venn diagram with three circles, each representing one of the three numbers.
3. Place the factors of each number in the respective circle.
4. Take the factors present in overlapping section of given numbers.
5. Multiply these factors to find the HCF.
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