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HCF of 867 and 225

HCF of 867 and 225 is the largest possible number that divides 867 and 225 exactly without any remainder. The factors of 867 and 225 are 1, 3, 17, 51, 289, 867 and 1, 3, 5, 9, 15, 25, 45, 75, 225 respectively. There are 3 commonly used methods to find the HCF of 867 and 225 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 867 and 225
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 867 and 225?

Answer: HCF of 867 and 225 is 3.

Explanation:

The HCF of two non-zero integers, x(867) and y(225), is the highest positive integer m(3) that divides both x(867) and y(225) without any remainder.

Methods to Find HCF of 867 and 225

The methods to find the HCF of 867 and 225 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

HCF of 867 and 225 by Listing Common Factors

Factors of 867: 1, 3, 17, 51, 289, 867
Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225

There are 2 common factors of 867 and 225, that are 1 and 3. Therefore, the highest common factor of 867 and 225 is 3.

HCF of 867 and 225 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 = 867 and Y = 225

HCF(867, 225) = HCF(225, 867 mod 225) = HCF(225, 192)
HCF(225, 192) = HCF(192, 225 mod 192) = HCF(192, 33)
HCF(192, 33) = HCF(33, 192 mod 33) = HCF(33, 27)
HCF(33, 27) = HCF(27, 33 mod 27) = HCF(27, 6)
HCF(27, 6) = HCF(6, 27 mod 6) = HCF(6, 3)
HCF(6, 3) = HCF(3, 6 mod 3) = HCF(3, 0)
HCF(3, 0) = 3 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 867 and 225 is 3.

HCF of 867 and 225 by Long Division

HCF of 867 and 225 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 867 (larger number) by 225 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (225) by the remainder (192).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the HCF of 867 and 225.

☛ Also Check:

HCF of 867 and 225 Examples

Example 1: For two numbers, HCF = 3 and LCM = 65025. If one number is 867, find the other number.

Solution:

Given: HCF (y, 867) = 3 and LCM (y, 867) = 65025
∵ HCF × LCM = 867 × (y)
⇒ y = (HCF × LCM)/867
⇒ y = (3 × 65025)/867
⇒ y = 225
Therefore, the other number is 225.
Example 2: The product of two numbers is 195075. If their HCF is 3, what is their LCM?

Solution:

Given: HCF = 3 and product of numbers = 195075
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 195075/3
Therefore, the LCM is 65025.
Example 3: Find the HCF of 867 and 225, if their LCM is 65025.

Solution:

∵ LCM × HCF = 867 × 225
⇒ HCF(867, 225) = (867 × 225)/65025 = 3
Therefore, the highest common factor of 867 and 225 is 3.

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FAQs on HCF of 867 and 225

What is the HCF of 867 and 225?

The HCF of 867 and 225 is 3. To calculate the HCF (Highest Common Factor) of 867 and 225, we need to factor each number (factors of 867 = 1, 3, 17, 51, 289, 867; factors of 225 = 1, 3, 5, 9, 15, 25, 45, 75, 225) and choose the highest factor that exactly divides both 867 and 225, i.e., 3.

How to Find the HCF of 867 and 225 by Prime Factorization?

To find the HCF of 867 and 225, we will find the prime factorization of the given numbers, i.e. 867 = 3 × 17 × 17; 225 = 3 × 3 × 5 × 5.
⇒ Since 3 is the only common prime factor of 867 and 225. Hence, HCF (867, 225) = 3.
☛ Prime Number

What is the Relation Between LCM and HCF of 867, 225?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 867 and 225, i.e. HCF × LCM = 867 × 225.

What are the Methods to Find HCF of 867 and 225?

There are three commonly used methods to find the HCF of 867 and 225.

By Listing Common Factors
By Prime Factorization
By Long Division

If the HCF of 225 and 867 is 3, Find its LCM.

HCF(225, 867) × LCM(225, 867) = 225 × 867
Since the HCF of 225 and 867 = 3
⇒ 3 × LCM(225, 867) = 195075
Therefore, LCM = 65025
☛ Highest Common Factor Calculator

How to Find the HCF of 867 and 225 by Long Division Method?

To find the HCF of 867, 225 using long division method, 867 is divided by 225. The corresponding divisor (3) when remainder equals 0 is taken as HCF.

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