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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 Exponents Using 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 Exponents

HCF Method
Calculate HCF
30
=
2
1
×
3
1
×
5
1
75
=
3
1
×
5
2

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 60 and 75.
Solution:
Prime factorization of 60: 60 = 2, 2, 3, 5.
Prime factorization of 75: 75 = 3, 5, 5.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(60, 75) = 15. Example 2: Find the HCF of 36 and 42.
Solution:
Prime factorization of 36: 36 = 2, 2, 3, 3.
Prime factorization of 42: 42 = 2, 3, 7.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(36, 42) = 6. Example 3: Find the HCF of 36 and 90.
Solution:
Prime factorization of 36: 36 = 2, 2, 3, 3.
Prime factorization of 90: 90 = 2, 3, 3, 5.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(36, 90) = 18.

Exercise

1. HCF(18,27) = 9
 2. HCF(32,48) = 16
 3. HCF(56,72) = 8
 4. HCF(56,70) = 14
 5. HCF(72,84) = 12
 6. HCF(75,50) = 25
 7. HCF(45,90) = 45
 8. HCF(24,36) = 12
 9. HCF(16,96) = 16
 10. HCF(12,15) = 3

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 division to find the prime factorization of each number.
2. Write the prime factors using exponents.
3. Identify common factors with lowest exponent.
4. Multiply these these factors with their exponent to find the HCF.
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