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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 Multiple Numbers By Exponents Using Factor Tree

Multiple Numbers Two Numbers Three Numbers
Method
Exponents Prime Factorization Listing Ladder Division
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Answer: HCF of 18, 24, 54, 60 is 6

Step A: Find the Factors Using Factor Tree

Factor Methods
Factors of 18
18
↙
↘
2
9
↙
↘
3
3
Factors of 24
24
↙
↘
2
12
↙
↘
2
6
↙
↘
2
3
Factors of 54
54
↙
↘
2
27
↙
↘
3
9
↙
↘
3
3
Factors of 60
60
↙
↘
2
30
↙
↘
2
15
↙
↘
3
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 Exponents

HCF Method
Calculate HCF
18
=
2
1
×
3
2
24
=
2
3
×
3
1
54
=
2
1
×
3
3
60
=
2
2
×
3
1
×
5
1

Exponents Help

1. List the prime factors.
2. Identify common prime factors.
3. Select factors with lowest power.
4. Multiply to Find HCF.

What is Exponents?

Exponents method simplifies finding the highest common factor or HCF by listing all the prime factors of each number and then selecting the lowest power of each common prime factor to obtain the HCF.

Solved Examples

Examples

Example 1: Find the HCF of 4 and 6.
Solution:
Prime factorization of 4: 4 = 2, 2.
Prime factorization of 6: 6 = 2, 3.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(4, 6) = 2. Example 2: Find the HCF of 6 and 9.
Solution:
Prime factorization of 6: 6 = 2, 3.
Prime factorization of 9: 9 = 3, 3.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(6, 9) = 3. Example 3: Find the HCF of 8 and 12.
Solution:
Prime factorization of 8: 8 = 2, 2, 2.
Prime factorization of 12: 12 = 2, 2, 3.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(8, 12) = 4.

Exercise

1. HCF(75,100,125) = 25
 2. HCF(49,98,147) = 49
 3. HCF(21,28,35) = 7
 4. HCF(8,24,40) = 8
 5. HCF(16,24,32) = 8
 6. HCF(14,21,28) = 7
 7. HCF(36, 48, 96) = 12
 8. HCF(25,30,40) = 5
 9. HCF(9,12,15) = 3
 10. HCF(12,18,24) = 6

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 factorization of each number.
3. Take common prime factors with their respective exponents.
4. Select the those prime factors that have the lowest power.
5. Multiply these factors to find the HCF.
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