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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 Multiplication

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

Step A: Find the Factors Using All Factors By Multiplication

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

All Factors By Multiplication Help

1. Start from Number 1.
2. Verify multiplication of pairs.
3. It must equal to number.
4. Continue pairing.
5. Until square root of number.
6. These pairs represent all factors.

What is All Factors By Multiplication?

In the multiplication method for finding factors, we identify the pairs of numbers that multiply together to equal the given number. These pairs represent the factors of the number.

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 20 and 60.
Solution:
Factors of 20 = 1, 2, 4, 5, 10, 20.
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Take the highest common factor.
Here, 20 is the highest common factor of 20 and 60.
Therefore, HCF(20, 60) = 20. Example 2: Find the HCF of 15 and 45.
Solution:
Factors of 15 = 1, 3, 5, 15.
Factors of 45 = 1, 3, 5, 9, 15, 45.
Take the highest common factor.
Here, 15 is the highest common factor of 15 and 45.
Therefore, HCF(15, 45) = 15. Example 3: Find the HCF of 12 and 8.
Solution:
Factors of 12 = 1, 2, 3, 4, 6, 12.
Factors of 8 = 1, 2, 4, 8.
Take the highest common factor.
Here, 4 is the highest common factor of 12 and 8.
Therefore, HCF(12, 8) = 4.

Exercise

1. HCF(24,36) = 12
 2. HCF(18,27) = 9
 3. HCF(48,64) = 16
 4. HCF(45,50) = 5
 5. HCF(12,28) = 4
 6. HCF(120,150) = 30
 7. HCF(18,30) = 6
 8. HCF(30,40) = 10
 9. HCF(56,42) = 14
 10. HCF(27,63) = 9

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 factors of each number using all factors by multiplication.
2. If multiplication is given number then both multipliers and multiplicand 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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