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HCF of 1095 and 1168

HCF of 1095 and 1168 is the largest possible number that divides 1095 and 1168 exactly without any remainder. The factors of 1095 and 1168 are 1, 3, 5, 15, 73, 219, 365, 1095 and 1, 2, 4, 8, 16, 73, 146, 292, 584, 1168 respectively. There are 3 commonly used methods to find the HCF of 1095 and 1168 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 1095 and 1168
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 1095 and 1168?

Answer: HCF of 1095 and 1168 is 73.

Explanation:

The HCF of two non-zero integers, x(1095) and y(1168), is the highest positive integer m(73) that divides both x(1095) and y(1168) without any remainder.

Methods to Find HCF of 1095 and 1168

The methods to find the HCF of 1095 and 1168 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 1095 and 1168 by Long Division

HCF of 1095 and 1168 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 1168 (larger number) by 1095 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (1095) by the remainder (73).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (73) is the HCF of 1095 and 1168.

HCF of 1095 and 1168 by Listing Common Factors

Factors of 1095: 1, 3, 5, 15, 73, 219, 365, 1095
Factors of 1168: 1, 2, 4, 8, 16, 73, 146, 292, 584, 1168

There are 2 common factors of 1095 and 1168, that are 73 and 1. Therefore, the highest common factor of 1095 and 1168 is 73.

HCF of 1095 and 1168 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 = 1168 and Y = 1095

HCF(1168, 1095) = HCF(1095, 1168 mod 1095) = HCF(1095, 73)
HCF(1095, 73) = HCF(73, 1095 mod 73) = HCF(73, 0)
HCF(73, 0) = 73 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 1095 and 1168 is 73.

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HCF of 1095 and 1168 Examples

Example 1: Find the highest number that divides 1095 and 1168 exactly.

Solution:

The highest number that divides 1095 and 1168 exactly is their highest common factor, i.e. HCF of 1095 and 1168.
⇒ Factors of 1095 and 1168:
- Factors of 1095 = 1, 3, 5, 15, 73, 219, 365, 1095
- Factors of 1168 = 1, 2, 4, 8, 16, 73, 146, 292, 584, 1168
Therefore, the HCF of 1095 and 1168 is 73.
Example 2: The product of two numbers is 1278960. If their HCF is 73, what is their LCM?

Solution:

Given: HCF = 73 and product of numbers = 1278960
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1278960/73
Therefore, the LCM is 17520.
Example 3: For two numbers, HCF = 73 and LCM = 17520. If one number is 1095, find the other number.

Solution:

Given: HCF (x, 1095) = 73 and LCM (x, 1095) = 17520
∵ HCF × LCM = 1095 × (x)
⇒ x = (HCF × LCM)/1095
⇒ x = (73 × 17520)/1095
⇒ x = 1168
Therefore, the other number is 1168.

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FAQs on HCF of 1095 and 1168

What is the HCF of 1095 and 1168?

The HCF of 1095 and 1168 is 73. To calculate the HCF (Highest Common Factor) of 1095 and 1168, we need to factor each number (factors of 1095 = 1, 3, 5, 15, 73, 219, 365, 1095; factors of 1168 = 1, 2, 4, 8, 16, 73, 146, 292, 584, 1168) and choose the highest factor that exactly divides both 1095 and 1168, i.e., 73.

What are the Methods to Find HCF of 1095 and 1168?

There are three commonly used methods to find the HCF of 1095 and 1168.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the HCF of 1095 and 1168 by Long Division Method?

To find the HCF of 1095, 1168 using long division method, 1168 is divided by 1095. The corresponding divisor (73) when remainder equals 0 is taken as HCF.

If the HCF of 1168 and 1095 is 73, Find its LCM.

HCF(1168, 1095) × LCM(1168, 1095) = 1168 × 1095
Since the HCF of 1168 and 1095 = 73
⇒ 73 × LCM(1168, 1095) = 1278960
Therefore, LCM = 17520
☛ Highest Common Factor Calculator

How to Find the HCF of 1095 and 1168 by Prime Factorization?

To find the HCF of 1095 and 1168, we will find the prime factorization of the given numbers, i.e. 1095 = 3 × 5 × 73; 1168 = 2 × 2 × 2 × 2 × 73.
⇒ Since 73 is the only common prime factor of 1095 and 1168. Hence, HCF (1095, 1168) = 73.
☛ Prime Numbers

What is the Relation Between LCM and HCF of 1095, 1168?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 1095 and 1168, i.e. HCF × LCM = 1095 × 1168.

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