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HCF
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HCF of Multiple Numbers By Exponents Using Ladder

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Answer: HCF of 18, 24, 54, 60 is 6
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Step A: Find the Factors Using Ladder

Factor Methods
Factors of 18
18
/ 2
9
/ 3
3
/ 3
1
Factors of 24
24
/ 2
12
/ 2
6
/ 2
3
/ 3
1
Factors of 54
54
/ 2
27
/ 3
9
/ 3
3
/ 3
1
Factors of 60
60
/ 2
30
/ 2
15
/ 3
5
/ 5
1

Ladder Help

1. Start with smallest prime factor.
2. Divide the number by it.
3. Write prime factor on right.
4. Place the quotient below.
5. Repeat with same prime factor.
6. Move to next prime factor if not divisible.
7. Continue until 1.
8. Numbers on the right are prime factors.

What is Ladder?

The ladder method involves repeatedly dividing the number by the smallest prime numbers, starting from 2 until the quotient becomes 1. The divisors are arranged in a ladder formation, hence the method name is ladder.

Step B: Find the HCF Using Exponents

HCF Method
Calculate HCF
18
=
2
1
×
3
2
24
=
2
3
×
3
1
54
=
2
1
×
3
3
60
=
2
2
×
3
1
×
5
1

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 14 and 21.
Solution:
Prime factorization of 14: 14 = 2, 7.
Prime factorization of 21: 21 = 3, 7.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(14, 21) = 7. Example 2: Find the HCF of 18 and 24.
Solution:
Prime factorization of 18: 18 = 2, 3, 3.
Prime factorization of 24: 24 = 2, 2, 2, 3.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(18, 24) = 6. Example 3: Find the HCF of 8 and 12.
Solution:
Prime factorization of 8: 8 = 2, 2, 2.
Prime factorization of 12: 12 = 2, 2, 3.
Take the smallest power of common prime factors and multiply them together to get the HCF.
Therefore, HCF(8, 12) = 4.

Exercise

1. HCF(36,48,60) = 12. 2. HCF(40,60,80) = 20. 3. HCF(20,35) = 5. 4. HCF(15,25,35) = 5. 5. HCF(10,20,30) = 10. 6. HCF(15,20,25,30) = 5. 7. HCF(3,6,18) = 3. 8. HCF(6,9,15,18) = 3. 9. HCF(8,24,60) = 4. 10. HCF(12,18,24) = 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. Write down the given numbers.
2. Use the ladder method to find the prime factors of each number.
3. Write down common prime factors with their respective exponents.
4. Select the those prime factors that have the lowest power.
5. Multiply these factors to find the HCF.
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