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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 Factor Tree

Three Numbers Two Numbers Multiple Numbers
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Division
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Answer: HCF of 12, 18, 24 is 6

Step A: Find the Factors Using Factor Tree

Factor Methods
Factors of 12
12
↙
↘
2
6
↙
↘
2
3
Factors of 18
18
↙
↘
2
9
↙
↘
3
3
Factors of 24
24
↙
↘
2
12
↙
↘
2
6
↙
↘
2
3

Factor Tree Help

1. Always begin with smallest prime.
2. This is the left child of given node.
3. Divide the number by that prime
4. Quotient is the right child of that node.
5. Repeat until right becomes prime factor.
6. Keep tree structure organized.

What is Factor Tree?

The factor tree method is a visual approach used to find the prime factorization of a composite number. It involves breaking down a number into its prime factors by repeatedly dividing it into smaller prime factors until only prime numbers remain which is represent in tree structure.

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(75,100,125) = 25
 2. HCF(25,35,45) = 5
 3. HCF(21,28,35) = 7
 4. HCF(16, 24, 32) = 8
 5. HCF(81, 108, 135) = 27
 6. HCF(60, 80, 10) = 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. Write down the given numbers.
2. Use the factor tree method to find the prime factors of each number.
3. Represent the prime factors in the Venn diagram.
4. Take the factors present in overlapping section of given numbers.
5. Multiply these factors to find the HCF.
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