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HCF of 255 and 867

HCF of 255 and 867 is the largest possible number that divides 255 and 867 exactly without any remainder. The factors of 255 and 867 are 1, 3, 5, 15, 17, 51, 85, 255 and 1, 3, 17, 51, 289, 867 respectively. There are 3 commonly used methods to find the HCF of 255 and 867 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 255 and 867
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 255 and 867?

Answer: HCF of 255 and 867 is 51.

Explanation:

The HCF of two non-zero integers, x(255) and y(867), is the highest positive integer m(51) that divides both x(255) and y(867) without any remainder.

Methods to Find HCF of 255 and 867

The methods to find the HCF of 255 and 867 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

HCF of 255 and 867 by Listing Common Factors

Factors of 255: 1, 3, 5, 15, 17, 51, 85, 255
Factors of 867: 1, 3, 17, 51, 289, 867

There are 4 common factors of 255 and 867, that are 1, 3, 17, and 51. Therefore, the highest common factor of 255 and 867 is 51.

HCF of 255 and 867 by Prime Factorization

Prime factorization of 255 and 867 is (3 × 5 × 17) and (3 × 17 × 17) respectively. As visible, 255 and 867 have common prime factors. Hence, the HCF of 255 and 867 is 3 × 17 = 51.

HCF of 255 and 867 by Long Division

HCF of 255 and 867 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 867 (larger number) by 255 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (255) by the remainder (102).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (51) is the HCF of 255 and 867.

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HCF of 255 and 867 Examples

Example 1: Find the highest number that divides 255 and 867 exactly.

Solution:

The highest number that divides 255 and 867 exactly is their highest common factor, i.e. HCF of 255 and 867.
⇒ Factors of 255 and 867:
- Factors of 255 = 1, 3, 5, 15, 17, 51, 85, 255
- Factors of 867 = 1, 3, 17, 51, 289, 867
Therefore, the HCF of 255 and 867 is 51.
Example 2: The product of two numbers is 221085. If their HCF is 51, what is their LCM?

Solution:

Given: HCF = 51 and product of numbers = 221085
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 221085/51
Therefore, the LCM is 4335.
Example 3: For two numbers, HCF = 51 and LCM = 4335. If one number is 255, find the other number.

Solution:

Given: HCF (y, 255) = 51 and LCM (y, 255) = 4335
∵ HCF × LCM = 255 × (y)
⇒ y = (HCF × LCM)/255
⇒ y = (51 × 4335)/255
⇒ y = 867
Therefore, the other number is 867.

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FAQs on HCF of 255 and 867

What is the HCF of 255 and 867?

The HCF of 255 and 867 is 51. To calculate the Highest common factor (HCF) of 255 and 867, we need to factor each number (factors of 255 = 1, 3, 5, 15, 17, 51, 85, 255; factors of 867 = 1, 3, 17, 51, 289, 867) and choose the highest factor that exactly divides both 255 and 867, i.e., 51.

If the HCF of 867 and 255 is 51, Find its LCM.

HCF(867, 255) × LCM(867, 255) = 867 × 255
Since the HCF of 867 and 255 = 51
⇒ 51 × LCM(867, 255) = 221085
Therefore, LCM = 4335
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What is the Relation Between LCM and HCF of 255, 867?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 255 and 867, i.e. HCF × LCM = 255 × 867.

How to Find the HCF of 255 and 867 by Prime Factorization?

To find the HCF of 255 and 867, we will find the prime factorization of the given numbers, i.e. 255 = 3 × 5 × 17; 867 = 3 × 17 × 17.
⇒ Since 3, 17 are common terms in the prime factorization of 255 and 867. Hence, HCF(255, 867) = 3 × 17 = 51
☛ What is a Prime Number?

How to Find the HCF of 255 and 867 by Long Division Method?

To find the HCF of 255, 867 using long division method, 867 is divided by 255. The corresponding divisor (51) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 255 and 867?

There are three commonly used methods to find the HCF of 255 and 867.

By Long Division
By Prime Factorization
By Euclidean Algorithm

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