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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 Division

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

Step A: Find the Factors Using Division

Factor Methods
Factors of 12
2
12
12/2=6
2
6
⤶
6/2=3
3
3
⤶
3/3=1
1
⤶
Factors of 18
2
18
18/2=9
3
9
⤶
9/3=3
3
3
⤶
3/3=1
1
⤶
Factors of 24
2
24
24/2=12
2
12
⤶
12/2=6
2
6
⤶
6/2=3
3
3
⤶
3/3=1
1
⤶

Division Help

1. Start with the smallest prime.
2. Divide the number by this prime.
3. Write the quotient below.
4. Repeat until the quotient is 1.
5. Confirm using multiplication.

What is Division?

The division method for finding factors begins by dividing the given number by the smallest prime factor like 2, 3,.. This process is repeated with successive primes until the quotient is 1.

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 24, 36 and 48.
Solution:
Prime factors of 24 = 2, 2, 2, 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 = 2, 2, 3.
Therefore, HCF(24, 36, 48) = 12. Example 2: Find the HCF of 18, 30 and 42.
Solution:
Prime factors of 18 = 2, 3, 3
Prime factors of 30 = 2, 3, 5
Multiply factors present in the common region of venn diagram to find the HCF.
Factors present in common region = 2, 3.
Therefore, HCF(18, 30, 42) = 6. Example 3: Find the HCF of 56, 72 and 84.
Solution:
Prime factors of 56 = 2, 2, 2, 7
Prime factors of 72 = 2, 2, 2, 3, 3
Multiply factors present in the common region of venn diagram to find the HCF.
Factors present in common region = 2, 2.
Therefore, HCF(56, 72, 84) = 28.

Exercise

1. HCF(12,18,24) = 6
 2. HCF(64,96,128) = 32
 3. HCF(54,81,108) = 27
 4. HCF(20, 40, 60) = 20
 5. HCF(15, 25, 35) = 5
 6. HCF(63, 81, 99) = 9
 7. HCF(54, 66, 78) = 6
 8. HCF(32, 48, 64) = 16
 9. HCF(80, 100, 120) = 20
 10. HCF(90, 120, 150) = 30

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 division 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 all numbers.
5. Multiply these factors to find the HCF.
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