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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 Prime Factorization Using Factor Tree

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

Step A: Find the Factors Using Factor Tree

Factor Methods
Factors of 30
30
↙
↘
2
15
↙
↘
3
5
Factors of 75
75
↙
↘
3
25
↙
↘
5
5

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 Prime Factorization

HCF Method
Calculate HCF
30
=
2
×
3
×
5
75
=
3
×
5
×
5
HCF
=
3
x
5
=
15

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 24 and 36.
Solution:
Prime factorization of 24: 24 = 2, 2, 2, 3
Prime factorization of 36: 36 = 2, 2, 3, 3
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(24, 36) = 12. 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 36 and 45.
Solution:
Prime factorization of 36: 36 = 2, 2, 3, 3
Prime factorization of 45: 45 = 3, 3, 5
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(36, 45) = 9.

Exercise

1. HCF(18,27) = 9
 2. HCF(45,60) = 15
 3. HCF(32,48) = 16
 4. HCF(84,105) = 21
 5. HCF(72, 90) = 18
 6. HCF(60,72) = 12
 7. HCF(56,84) = 28
 8. HCF(17,89) = 1
 9. HCF(315,495) = 45
 10. HCF(60,20) = 20

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. Use factor tree for prime factorization.
2. Look for the prime factors that appear in both factor tree.
3. These are the common prime factors shared by both number.
4. Multiply together all the common prime factors identified.
5. This product represents the HCF of the two numbers.
6. Verify the HCF by dividing with numbers without leaving a remainder.
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