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HCF of 135 and 225

HCF of 135 and 225 is the largest possible number that divides 135 and 225 exactly without any remainder. The factors of 135 and 225 are 1, 3, 5, 9, 15, 27, 45, 135 and 1, 3, 5, 9, 15, 25, 45, 75, 225 respectively. There are 3 commonly used methods to find the HCF of 135 and 225 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 135 and 225
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 135 and 225?

Answer: HCF of 135 and 225 is 45.

Explanation:

The HCF of two non-zero integers, x(135) and y(225), is the highest positive integer m(45) that divides both x(135) and y(225) without any remainder.

Methods to Find HCF of 135 and 225

Let's look at the different methods for finding the HCF of 135 and 225.

Long Division Method
Prime Factorization Method
Listing Common Factors

HCF of 135 and 225 by Long Division

HCF of 135 and 225 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 225 (larger number) by 135 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (135) by the remainder (90).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (45) is the HCF of 135 and 225.

HCF of 135 and 225 by Prime Factorization

Prime factorization of 135 and 225 is (3 × 3 × 3 × 5) and (3 × 3 × 5 × 5) respectively. As visible, 135 and 225 have common prime factors. Hence, the HCF of 135 and 225 is 3 × 3 × 5 = 45.

HCF of 135 and 225 by Listing Common Factors

Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135
Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225

There are 6 common factors of 135 and 225, that are 1, 3, 5, 9, 45, and 15. Therefore, the highest common factor of 135 and 225 is 45.

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HCF of 135 and 225 Examples

Example 1: For two numbers, HCF = 45 and LCM = 675. If one number is 135, find the other number.

Solution:

Given: HCF (x, 135) = 45 and LCM (x, 135) = 675
∵ HCF × LCM = 135 × (x)
⇒ x = (HCF × LCM)/135
⇒ x = (45 × 675)/135
⇒ x = 225
Therefore, the other number is 225.
Example 2: Find the highest number that divides 135 and 225 exactly.

Solution:

The highest number that divides 135 and 225 exactly is their highest common factor, i.e. HCF of 135 and 225.
⇒ Factors of 135 and 225:
- Factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135
- Factors of 225 = 1, 3, 5, 9, 15, 25, 45, 75, 225
Therefore, the HCF of 135 and 225 is 45.
Example 3: The product of two numbers is 30375. If their HCF is 45, what is their LCM?

Solution:

Given: HCF = 45 and product of numbers = 30375
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 30375/45
Therefore, the LCM is 675.

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FAQs on HCF of 135 and 225

What is the HCF of 135 and 225?

The HCF of 135 and 225 is 45. To calculate the Highest common factor (HCF) of 135 and 225, we need to factor each number (factors of 135 = 1, 3, 5, 9, 15, 27, 45, 135; factors of 225 = 1, 3, 5, 9, 15, 25, 45, 75, 225) and choose the highest factor that exactly divides both 135 and 225, i.e., 45.

If the HCF of 225 and 135 is 45, Find its LCM.

HCF(225, 135) × LCM(225, 135) = 225 × 135
Since the HCF of 225 and 135 = 45
⇒ 45 × LCM(225, 135) = 30375
Therefore, LCM = 675
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What is the Relation Between LCM and HCF of 135, 225?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 135 and 225, i.e. HCF × LCM = 135 × 225.

How to Find the HCF of 135 and 225 by Long Division Method?

To find the HCF of 135, 225 using long division method, 225 is divided by 135. The corresponding divisor (45) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 135 and 225?

There are three commonly used methods to find the HCF of 135 and 225.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the HCF of 135 and 225 by Prime Factorization?

To find the HCF of 135 and 225, we will find the prime factorization of the given numbers, i.e. 135 = 3 × 3 × 3 × 5; 225 = 3 × 3 × 5 × 5.
⇒ Since 3, 3, 5 are common terms in the prime factorization of 135 and 225. Hence, HCF(135, 225) = 3 × 3 × 5 = 45
☛ What is a Prime Number?

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