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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 Listing Using All Factors By Division

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

Step A: Find the Factors Using All Factors By Division

Factor Methods
Factors of 30
30
÷
1
=
30
✅
30
÷
2
=
15
✅
30
÷
3
=
10
✅
30
÷
4
=
7.50
❌
30
÷
5
=
6
✅
30
÷
6
=
5
⮥
Factors of 75
75
÷
1
=
75
✅
75
÷
2
=
37.50
❌
75
÷
3
=
25
✅
75
÷
4
=
18.75
❌
75
÷
5
=
15
✅
75
÷
15
=
5
⮥

All Factors By Division Help

1. Begin from 1 and divide.
2. If remainder is 0.
3. Both divisor and quotient are factors.
4. Repeat for all integers.
5. Only up to square root.

What is All Factors By Division?

The division method for finding factors involves dividing the given number by each integer, starting from 1, up to the square root of the number. Factors are the divisors that yield a whole number quotient with no remainder.

Step B: Find the HCF Using Listing

HCF Method
Calculate HCF
Factors of 30:
1
2
3
5
6
10
15
30
Factors of 75:
1
3
5
15
25
75

Listing Help

1. List factors of each number.
2. Identify common factors.
3. If no common factors, HCF is 1.
4. Otherwise, select the highest one.

What is Listing?

The listing method for finding the Highest Common Factor or HCF involves listing all factors of each number, including 1 and the number itself. The biggest common factor is the HCF of the given numbers.

Solved Examples

Examples

Example 1: Find the HCF of 72 and 84.
Solution:
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Take the highest common factor.
Here, 12 is the highest common factor of 72 and 84.
Therefore, HCF(72, 84) = 12. Example 2: Find the HCF of 18 and 24.
Solution:
Factors of 18 = 1, 2, 3, 6, 9, 18.
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Take the highest common factor.
Here, 6 is the highest common factor of 18 and 24.
Therefore, HCF(18, 24) = 6. Example 3: Find the HCF of 25 and 75.
Solution:
Factors of 25 = 1, 5, 25.
Factors of 75 = 1, 3, 5, 15, 25, 75.
Take the highest common factor.
Here, 25 is the highest common factor of 25 and 75.
Therefore, HCF(25, 75) = 25.

Exercise

1. HCF(18,27) = 9
 2. HCF(45,60) = 15
 3. HCF(32,48) = 16
 4. HCF(24,36) = 12
 5. HCF(60,75) = 15
 6. HCF(36,42) = 6
 7. HCF(16,32) = 16
 8. HCF(16,20) = 4
 9. HCF(19,25) = 1
 10. HCF(75,80) = 5

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. Start by finding the factors of each number using all factors by division.
2. In this case, divisor and quotient both are factors of number.
3. List the factors of given numbers.
4. Look for the common factors.
5. Select the highest factor which represents the HCF of numbers.
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