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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 Division

Multiple Numbers Two Numbers Three Numbers
Method
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Answer: HCF of 18, 24, 54, 60 is 6

Step A: Find the Factors Using Division

Factor Methods
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
⤶
Factors of 54
2
54
54/2=27
3
27
⤶
27/3=9
3
9
⤶
9/3=3
3
3
⤶
3/3=1
1
⤶
Factors of 60
2
60
60/2=30
2
30
⤶
30/2=15
3
15
⤶
15/3=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 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 9 and 15.
Solution:
Prime factorization of 9: 9 = 3, 3.
Prime factorization of 15: 15 = 3, 5.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(9, 15) = 3. 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 smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(18, 24) = 6. Example 3: Find the HCF of 21 and 28.
Solution:
Prime factorization of 21: 21 = 3, 7.
Prime factorization of 28: 28 = 2, 2, 7.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(21, 28) = 7.

Exercise

1. HCF(75,100,125) = 25
 2. HCF(20,30) = 10
 3. HCF(63,84,105) = 21
 4. HCF(15,25,35) = 5
 5. HCF(16,24,32) = 8
 6. HCF(14,21,28) = 7
 7. HCF(36, 48, 96) = 12
 8. HCF(8,24,60) = 4
 9. HCF(15,18,24,30) = 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 division 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 lowest power.
5. Multiply these factors to find the HCF.
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