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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 Two Numbers By Venn Diagram Using Division

Two Numbers Three Numbers Multiple Numbers
Method
Venn Diagram Prime Factorization Listing Ladder Exponents Division
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Answer: HCF of 30, 75 is 15

Step A: Find the Factors Using Division

Factor Methods
Factors of 30
2
30
30/2=15
3
15
⤶
15/3=5
5
5
⤶
5/5=1
1
⤶
Factors of 75
3
75
75/3=25
5
25
⤶
25/5=5
5
5
⤶
5/5=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
2
5
3
5

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 60 and 20.
Solution:
We can write all the prime factors into the venn diagram for each number.
Prime factors of 60 = 2, 2, 3, 5
Prime factors of 20 = 2, 2, 5
Multiply factors present in the common region of venn diagram to find the HCF.
Factors present in common region = 2, 2, 5.
Therefore, HCF(60, 20) = 20. Example 2: Find the HCF of 27 and 63.
Solution:
We can write all the prime factors into the venn diagram for each number.
Prime factors of 27 = 3, 3, 3
Prime factors of 63 = 3, 3, 7
Multiply factors present in the common region of venn diagram to find the HCF.
Factors present in common region = 3, 3.
Therefore, HCF(27, 63) = 9. Example 3: Find the HCF of 48 and 18.
Solution:
We can write all the prime factors into the venn diagram for each number.
Prime factors of 48 = 2, 2, 2, 2, 3
Prime factors of 18 = 2, 3, 3
Multiply factors present in the common region of venn diagram to find the HCF.
Factors present in common region = 2, 3.
Therefore, HCF(48, 18) = 6.

Exercise

1. HCF(3,9) = 3
 2. HCF(40,60) = 20
 3. HCF(20,35) = 5
 4. HCF(24,104) = 8
 5. HCF(16,96) = 16
 6. HCF(24,60) = 12
 7. HCF(56, 140) = 28
 8. HCF(21, 49) = 7
 9. HCF(36,90) = 18
 10. HCF(56, 140) = 28

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 both numbers.
5. Multiply these factors to find the HCF.
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