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LCM
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HCF
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HCF of Two Numbers By Prime Factorization Using Ladder

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Answer: HCF of 30, 75 is 15
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Step A: Find the Factors Using Ladder

Factor Methods
Factors of 30
30
/ 2
15
/ 3
5
/ 5
1
Factors of 75
75
/ 3
25
/ 5
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 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 35 and 45.
Solution:
Prime factorization of 35: 35 = 5, 7
Prime factorization of 45: 45 = 3, 3, 5
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(35, 45) = 5. Example 2: Find the HCF of 30 and 75.
Solution:
Prime factorization of 30: 30 = 2, 3, 5
Prime factorization of 75: 75 = 3, 5, 5
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(30, 75) = 15. Example 3: Find the HCF of 21 and 49.
Solution:
Prime factorization of 21: 21 = 3, 7
Prime factorization of 49: 49 = 7, 7
Take the common prime factors and multiply them together to get HCF.
Therefore, HCF(21, 49) = 7.

Exercise

1. HCF(18,27) = 9. 2. HCF(36,42) = 6. 3. HCF(60,75) = 15. 4. HCF(56, 140) = 28. 5. HCF(84, 96) = 12. 6. HCF(60, 90) = 30. 7. HCF(28, 42) = 14. 8. HCF(48, 64) = 16. 9. HCF(38, 95) = 19. 10. HCF(15, 90) = 15.

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 ladder 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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