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HCF of 510 and 92

HCF of 510 and 92 is the largest possible number that divides 510 and 92 exactly without any remainder. The factors of 510 and 92 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510 and 1, 2, 4, 23, 46, 92 respectively. There are 3 commonly used methods to find the HCF of 510 and 92 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 510 and 92
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 510 and 92?

Answer: HCF of 510 and 92 is 2.

Explanation:

The HCF of two non-zero integers, x(510) and y(92), is the highest positive integer m(2) that divides both x(510) and y(92) without any remainder.

Methods to Find HCF of 510 and 92

Let's look at the different methods for finding the HCF of 510 and 92.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 510 and 92 by Prime Factorization

Prime factorization of 510 and 92 is (2 × 3 × 5 × 17) and (2 × 2 × 23) respectively. As visible, 510 and 92 have only one common prime factor i.e. 2. Hence, the HCF of 510 and 92 is 2.

HCF of 510 and 92 by Listing Common Factors

Factors of 510: 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
Factors of 92: 1, 2, 4, 23, 46, 92

There are 2 common factors of 510 and 92, that are 1 and 2. Therefore, the highest common factor of 510 and 92 is 2.

HCF of 510 and 92 by Long Division

HCF of 510 and 92 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 510 (larger number) by 92 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (92) by the remainder (50).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 510 and 92.

☛ Also Check:

HCF of 510 and 92 Examples

Example 1: For two numbers, HCF = 2 and LCM = 23460. If one number is 510, find the other number.

Solution:

Given: HCF (x, 510) = 2 and LCM (x, 510) = 23460
∵ HCF × LCM = 510 × (x)
⇒ x = (HCF × LCM)/510
⇒ x = (2 × 23460)/510
⇒ x = 92
Therefore, the other number is 92.
Example 2: Find the highest number that divides 510 and 92 exactly.

Solution:

The highest number that divides 510 and 92 exactly is their highest common factor, i.e. HCF of 510 and 92.
⇒ Factors of 510 and 92:
- Factors of 510 = 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
- Factors of 92 = 1, 2, 4, 23, 46, 92
Therefore, the HCF of 510 and 92 is 2.
Example 3: Find the HCF of 510 and 92, if their LCM is 23460.

Solution:

∵ LCM × HCF = 510 × 92
⇒ HCF(510, 92) = (510 × 92)/23460 = 2
Therefore, the highest common factor of 510 and 92 is 2.

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FAQs on HCF of 510 and 92

What is the HCF of 510 and 92?

The HCF of 510 and 92 is 2. To calculate the HCF (Highest Common Factor) of 510 and 92, we need to factor each number (factors of 510 = 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510; factors of 92 = 1, 2, 4, 23, 46, 92) and choose the highest factor that exactly divides both 510 and 92, i.e., 2.

How to Find the HCF of 510 and 92 by Long Division Method?

To find the HCF of 510, 92 using long division method, 510 is divided by 92. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 510 and 92?

There are three commonly used methods to find the HCF of 510 and 92.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the HCF of 510 and 92 by Prime Factorization?

To find the HCF of 510 and 92, we will find the prime factorization of the given numbers, i.e. 510 = 2 × 3 × 5 × 17; 92 = 2 × 2 × 23.
⇒ Since 2 is the only common prime factor of 510 and 92. Hence, HCF (510, 92) = 2.
☛ Prime Number

What is the Relation Between LCM and HCF of 510, 92?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 510 and 92, i.e. HCF × LCM = 510 × 92.

If the HCF of 92 and 510 is 2, Find its LCM.

HCF(92, 510) × LCM(92, 510) = 92 × 510
Since the HCF of 92 and 510 = 2
⇒ 2 × LCM(92, 510) = 46920
Therefore, LCM = 23460
☛ Highest Common Factor Calculator

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