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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 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 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 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. Example 2: 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 3: Find the HCF of 72 and 90.
Solution:
Prime factorization of 72: 72 = 2, 2, 2, 3, 3
Prime factorization of 90: 90 = 2, 3, 3, 5
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(72, 90) = 18.

Exercise

1. HCF(45,60) = 15
 2. HCF(32,48) = 16
 3. HCF(56,72) = 8
 4. HCF(60,72) = 12
 5. HCF(60,20) = 20
 6. HCF(18,24) = 6
 7. HCF(84,105) = 21
 8. HCF(30,45) = 15
 9. HCF(90,180) = 90
 10. HCF(100,150) = 50

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