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HCF of 186 and 403

HCF of 186 and 403 is the largest possible number that divides 186 and 403 exactly without any remainder. The factors of 186 and 403 are 1, 2, 3, 6, 31, 62, 93, 186 and 1, 13, 31, 403 respectively. There are 3 commonly used methods to find the HCF of 186 and 403 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 186 and 403
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 186 and 403?

Answer: HCF of 186 and 403 is 31.

Explanation:

The HCF of two non-zero integers, x(186) and y(403), is the highest positive integer m(31) that divides both x(186) and y(403) without any remainder.

Methods to Find HCF of 186 and 403

Let's look at the different methods for finding the HCF of 186 and 403.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 186 and 403 by Long Division

HCF of 186 and 403 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 403 (larger number) by 186 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (186) by the remainder (31).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (31) is the HCF of 186 and 403.

HCF of 186 and 403 by Listing Common Factors

Factors of 186: 1, 2, 3, 6, 31, 62, 93, 186
Factors of 403: 1, 13, 31, 403

There are 2 common factors of 186 and 403, that are 1 and 31. Therefore, the highest common factor of 186 and 403 is 31.

HCF of 186 and 403 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 = 403 and Y = 186

HCF(403, 186) = HCF(186, 403 mod 186) = HCF(186, 31)
HCF(186, 31) = HCF(31, 186 mod 31) = HCF(31, 0)
HCF(31, 0) = 31 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 186 and 403 is 31.

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HCF of 186 and 403 Examples

Example 1: For two numbers, HCF = 31 and LCM = 2418. If one number is 186, find the other number.

Solution:

Given: HCF (x, 186) = 31 and LCM (x, 186) = 2418
∵ HCF × LCM = 186 × (x)
⇒ x = (HCF × LCM)/186
⇒ x = (31 × 2418)/186
⇒ x = 403
Therefore, the other number is 403.
Example 2: Find the HCF of 186 and 403, if their LCM is 2418.

Solution:

∵ LCM × HCF = 186 × 403
⇒ HCF(186, 403) = (186 × 403)/2418 = 31
Therefore, the highest common factor of 186 and 403 is 31.
Example 3: Find the highest number that divides 186 and 403 exactly.

Solution:

The highest number that divides 186 and 403 exactly is their highest common factor, i.e. HCF of 186 and 403.
⇒ Factors of 186 and 403:
- Factors of 186 = 1, 2, 3, 6, 31, 62, 93, 186
- Factors of 403 = 1, 13, 31, 403
Therefore, the HCF of 186 and 403 is 31.

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FAQs on HCF of 186 and 403

What is the HCF of 186 and 403?

The HCF of 186 and 403 is 31. To calculate the Highest common factor of 186 and 403, we need to factor each number (factors of 186 = 1, 2, 3, 6, 31, 62, 93, 186; factors of 403 = 1, 13, 31, 403) and choose the highest factor that exactly divides both 186 and 403, i.e., 31.

How to Find the HCF of 186 and 403 by Long Division Method?

To find the HCF of 186, 403 using long division method, 403 is divided by 186. The corresponding divisor (31) when remainder equals 0 is taken as HCF.

If the HCF of 403 and 186 is 31, Find its LCM.

HCF(403, 186) × LCM(403, 186) = 403 × 186
Since the HCF of 403 and 186 = 31
⇒ 31 × LCM(403, 186) = 74958
Therefore, LCM = 2418
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What are the Methods to Find HCF of 186 and 403?

There are three commonly used methods to find the HCF of 186 and 403.

By Listing Common Factors
By Prime Factorization
By Long Division

What is the Relation Between LCM and HCF of 186, 403?

The following equation can be used to express the relation between LCM and HCF of 186 and 403, i.e. HCF × LCM = 186 × 403.

How to Find the HCF of 186 and 403 by Prime Factorization?

To find the HCF of 186 and 403, we will find the prime factorization of the given numbers, i.e. 186 = 2 × 3 × 31; 403 = 13 × 31.
⇒ Since 31 is the only common prime factor of 186 and 403. Hence, HCF (186, 403) = 31.
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