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HCF of 506 and 1155

HCF of 506 and 1155 is the largest possible number that divides 506 and 1155 exactly without any remainder. The factors of 506 and 1155 are 1, 2, 11, 22, 23, 46, 253, 506 and 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155 respectively. There are 3 commonly used methods to find the HCF of 506 and 1155 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 506 and 1155
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 506 and 1155?

Answer: HCF of 506 and 1155 is 11.

Explanation:

The HCF of two non-zero integers, x(506) and y(1155), is the highest positive integer m(11) that divides both x(506) and y(1155) without any remainder.

Methods to Find HCF of 506 and 1155

Let's look at the different methods for finding the HCF of 506 and 1155.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

HCF of 506 and 1155 by Listing Common Factors

Factors of 506: 1, 2, 11, 22, 23, 46, 253, 506
Factors of 1155: 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155

There are 2 common factors of 506 and 1155, that are 1 and 11. Therefore, the highest common factor of 506 and 1155 is 11.

HCF of 506 and 1155 by Long Division

HCF of 506 and 1155 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 1155 (larger number) by 506 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (506) by the remainder (143).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (11) is the HCF of 506 and 1155.

HCF of 506 and 1155 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 = 1155 and Y = 506

HCF(1155, 506) = HCF(506, 1155 mod 506) = HCF(506, 143)
HCF(506, 143) = HCF(143, 506 mod 143) = HCF(143, 77)
HCF(143, 77) = HCF(77, 143 mod 77) = HCF(77, 66)
HCF(77, 66) = HCF(66, 77 mod 66) = HCF(66, 11)
HCF(66, 11) = HCF(11, 66 mod 11) = HCF(11, 0)
HCF(11, 0) = 11 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 506 and 1155 is 11.

☛ Also Check:

HCF of 506 and 1155 Examples

Example 1: The product of two numbers is 584430. If their HCF is 11, what is their LCM?

Solution:

Given: HCF = 11 and product of numbers = 584430
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 584430/11
Therefore, the LCM is 53130.
Example 2: Find the highest number that divides 506 and 1155 exactly.

Solution:

The highest number that divides 506 and 1155 exactly is their highest common factor, i.e. HCF of 506 and 1155.
⇒ Factors of 506 and 1155:
- Factors of 506 = 1, 2, 11, 22, 23, 46, 253, 506
- Factors of 1155 = 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155
Therefore, the HCF of 506 and 1155 is 11.
Example 3: For two numbers, HCF = 11 and LCM = 53130. If one number is 506, find the other number.

Solution:

Given: HCF (y, 506) = 11 and LCM (y, 506) = 53130
∵ HCF × LCM = 506 × (y)
⇒ y = (HCF × LCM)/506
⇒ y = (11 × 53130)/506
⇒ y = 1155
Therefore, the other number is 1155.

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FAQs on HCF of 506 and 1155

What is the HCF of 506 and 1155?

The HCF of 506 and 1155 is 11. To calculate the Highest common factor (HCF) of 506 and 1155, we need to factor each number (factors of 506 = 1, 2, 11, 22, 23, 46, 253, 506; factors of 1155 = 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155) and choose the highest factor that exactly divides both 506 and 1155, i.e., 11.

What is the Relation Between LCM and HCF of 506, 1155?

The following equation can be used to express the relation between LCM and HCF of 506 and 1155, i.e. HCF × LCM = 506 × 1155.

How to Find the HCF of 506 and 1155 by Prime Factorization?

To find the HCF of 506 and 1155, we will find the prime factorization of the given numbers, i.e. 506 = 2 × 11 × 23; 1155 = 3 × 5 × 7 × 11.
⇒ Since 11 is the only common prime factor of 506 and 1155. Hence, HCF (506, 1155) = 11.
☛ What is a Prime Number?

If the HCF of 1155 and 506 is 11, Find its LCM.

HCF(1155, 506) × LCM(1155, 506) = 1155 × 506
Since the HCF of 1155 and 506 = 11
⇒ 11 × LCM(1155, 506) = 584430
Therefore, LCM = 53130
☛ HCF Calculator

How to Find the HCF of 506 and 1155 by Long Division Method?

To find the HCF of 506, 1155 using long division method, 1155 is divided by 506. The corresponding divisor (11) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 506 and 1155?

There are three commonly used methods to find the HCF of 506 and 1155.

By Long Division
By Prime Factorization
By Euclidean Algorithm

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