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HCF of 135 and 255

HCF of 135 and 255 is the largest possible number that divides 135 and 255 exactly without any remainder. The factors of 135 and 255 are 1, 3, 5, 9, 15, 27, 45, 135 and 1, 3, 5, 15, 17, 51, 85, 255 respectively. There are 3 commonly used methods to find the HCF of 135 and 255 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 135 and 255
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 135 and 255?

Answer: HCF of 135 and 255 is 15.

Explanation:

The HCF of two non-zero integers, x(135) and y(255), is the highest positive integer m(15) that divides both x(135) and y(255) without any remainder.

Methods to Find HCF of 135 and 255

Let's look at the different methods for finding the HCF of 135 and 255.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

HCF of 135 and 255 by Prime Factorization

Prime factorization of 135 and 255 is (3 × 3 × 3 × 5) and (3 × 5 × 17) respectively. As visible, 135 and 255 have common prime factors. Hence, the HCF of 135 and 255 is 3 × 5 = 15.

HCF of 135 and 255 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 255 and Y = 135

HCF(255, 135) = HCF(135, 255 mod 135) = HCF(135, 120)
HCF(135, 120) = HCF(120, 135 mod 120) = HCF(120, 15)
HCF(120, 15) = HCF(15, 120 mod 15) = HCF(15, 0)
HCF(15, 0) = 15 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 135 and 255 is 15.

HCF of 135 and 255 by Long Division

HCF of 135 and 255 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 255 (larger number) by 135 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (135) by the remainder (120).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (15) is the HCF of 135 and 255.

☛ Also Check:

HCF of 135 and 255 Examples

Example 1: Find the HCF of 135 and 255, if their LCM is 2295.

Solution:

∵ LCM × HCF = 135 × 255
⇒ HCF(135, 255) = (135 × 255)/2295 = 15
Therefore, the highest common factor of 135 and 255 is 15.
Example 2: Find the highest number that divides 135 and 255 exactly.

Solution:

The highest number that divides 135 and 255 exactly is their highest common factor, i.e. HCF of 135 and 255.
⇒ Factors of 135 and 255:
- Factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135
- Factors of 255 = 1, 3, 5, 15, 17, 51, 85, 255
Therefore, the HCF of 135 and 255 is 15.
Example 3: The product of two numbers is 34425. If their HCF is 15, what is their LCM?

Solution:

Given: HCF = 15 and product of numbers = 34425
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 34425/15
Therefore, the LCM is 2295.

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FAQs on HCF of 135 and 255

What is the HCF of 135 and 255?

The HCF of 135 and 255 is 15. To calculate the HCF of 135 and 255, we need to factor each number (factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135; factors of 255 = 1, 3, 5, 15, 17, 51, 85, 255) and choose the highest factor that exactly divides both 135 and 255, i.e., 15.

How to Find the HCF of 135 and 255 by Long Division Method?

To find the HCF of 135, 255 using long division method, 255 is divided by 135. The corresponding divisor (15) when remainder equals 0 is taken as HCF.

How to Find the HCF of 135 and 255 by Prime Factorization?

To find the HCF of 135 and 255, we will find the prime factorization of the given numbers, i.e. 135 = 3 × 3 × 3 × 5; 255 = 3 × 5 × 17.
⇒ Since 3, 5 are common terms in the prime factorization of 135 and 255. Hence, HCF(135, 255) = 3 × 5 = 15
☛ What is a Prime Number?

What are the Methods to Find HCF of 135 and 255?

There are three commonly used methods to find the HCF of 135 and 255.

By Long Division
By Prime Factorization
By Listing Common Factors

What is the Relation Between LCM and HCF of 135, 255?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 135 and 255, i.e. HCF × LCM = 135 × 255.

If the HCF of 255 and 135 is 15, Find its LCM.

HCF(255, 135) × LCM(255, 135) = 255 × 135
Since the HCF of 255 and 135 = 15
⇒ 15 × LCM(255, 135) = 34425
Therefore, LCM = 2295
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