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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 Ladder

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

Step B: Find the HCF Using Ladder

HCF Method
Calculate HCF
3
5
30
/ 3
10
/ 5
2
75
/ 3
25
/ 5
5

Ladder Help

1. Identify common factors.
2. Place common factors outside.
3. Divide each number.
4. Write quotient below.
5. Repeat until no common factors.
6. Multiply numbers on left side .
7. Obtain the HCF.

What is Ladder?

The ladder method for finding the HCF involves identifying common prime factors and dividing numbers until no more common factors are found. The process stops when no further division is possible, and the remaining divisors are multiplied to get the HCF.

Solved Examples

Examples

Example 1: Find the HCF of 36 and 72.
Solution:
Factors of 36: 2, 2, 3, 3
Factors of 72: 2, 2, 2, 3, 3
Common prime factors = 2, 2, 3, 3
HCF: Take only common prime factors and multiply them to get the HCF.
Therefore, HCF(36, 72) = 36. Example 2: Find the HCF of 12 and 30.
Solution:
Factors of 12: 2, 2, 3
Factors of 30: 2, 3, 5
Common prime factors = 2, 3
HCF: Take only common prime factors and multiply them to get the HCF.
Therefore, HCF(12, 30) = 6. Example 3: Find the HCF of 60 and 72.
Solution:
Factors of 60: 2, 2, 3, 5
Factors of 72: 2, 2, 2, 3, 3
Common prime factors = 2, 2, 3
HCF: Take only common prime factors and multiply them to get the HCF.
Therefore, HCF(60, 72) = 12.

Exercise

1. HCF(63,81) = 9
 2. HCF(35,70) = 35
 3. HCF(54,72) = 18
 4. HCF(16,40) = 8
 5. HCF(24,36) = 12
 6. HCF(24,60) = 12
 7. HCF(36,63) = 9
 8. HCF(30,50) = 10
 9. HCF(75,45) = 15
 10. HCF(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. Enter two numbers into the calculator.
2. Organize their prime factors in a ladder shape using Ladder Division.
3. Identify the common factors on the left side for both numbers.
4. Multiply these common prime factors together to get the HCF of the given numbers.
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