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HCF of 403, 434 and 465

HCF of 403, 434 and 465 is the largest possible number that divides 403, 434 and 465 exactly without any remainder. The factors of 403, 434 and 465 are (1, 13, 31, 403), (1, 2, 7, 14, 31, 62, 217, 434) and (1, 3, 5, 15, 31, 93, 155, 465) respectively. There are 3 commonly used methods to find the HCF of 403, 434 and 465 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 403, 434 and 465
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 403, 434 and 465?

Answer: HCF of 403, 434 and 465 is 31.

Explanation:

The HCF of three non-zero integers, x(403), y(434) and z(465), is the highest positive integer m(31) that divides x(403), y(434) and z(465) without any remainder.

Methods to Find HCF of 403, 434 and 465

The methods to find the HCF of 403, 434 and 465 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Prime Factorization Method

HCF of 403, 434 and 465 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.

HCF(403, 434, 465) = HCF(HCF(403, 434), 465)

HCF(434, 403) = HCF(403, 434 mod 403) = HCF(403, 31)
HCF(403, 31) = HCF(31, 403 mod 31) = HCF(31, 0)
HCF(31, 0) = 31 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(31, 465)

HCF(465, 31) = HCF(31, 465 mod 31) = HCF(31, 0)
HCF(31, 0) = 31 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 403, 434 and 465 is 31.

HCF of 403, 434 and 465 by Listing Common Factors

Factors of 403: 1, 13, 31, 403
Factors of 434: 1, 2, 7, 14, 31, 62, 217, 434
Factors of 465: 1, 3, 5, 15, 31, 93, 155, 465

There are 2 common factors of 403, 434 and 465, that are 1 and 31. Therefore, the highest common factor of 403, 434 and 465 is 31.

HCF of 403, 434 and 465 by Prime Factorization

Prime factorization of 403, 434 and 465 is (13 × 31), (2 × 7 × 31) and (3 × 5 × 31) respectively. As visible, 403, 434 and 465 have only one common prime factor i.e. 31. Hence, the HCF of 403, 434 and 465 is 31.

☛ Also Check:

HCF of 403, 434 and 465 Examples

Example 1: Find the highest number that divides 403, 434, and 465 completely.

Solution:

The highest number that divides 403, 434, and 465 exactly is their highest common factor.
- Factors of 403 = 1, 13, 31, 403
- Factors of 434 = 1, 2, 7, 14, 31, 62, 217, 434
- Factors of 465 = 1, 3, 5, 15, 31, 93, 155, 465
The HCF of 403, 434, and 465 is 31.
∴ The highest number that divides 403, 434, and 465 is 31.
Example 2: Calculate the HCF of 403, 434, and 465 using LCM of the given numbers.

Solution:

Prime factorization of 403, 434 and 465 is given as,
- 403 = 13 × 31
- 434 = 2 × 7 × 31
- 465 = 3 × 5 × 31
LCM(403, 434) = 5642, LCM(434, 465) = 6510, LCM(465, 403) = 6045, LCM(403, 434, 465) = 84630
⇒ HCF(403, 434, 465) = [(403 × 434 × 465) × LCM(403, 434, 465)]/[LCM(403, 434) × LCM (434, 465) × LCM(465, 403)]
⇒ HCF(403, 434, 465) = (81329430 × 84630)/(5642 × 6510 × 6045)
⇒ HCF(403, 434, 465) = 31.
Therefore, the HCF of 403, 434 and 465 is 31.
Example 3: Verify the relation between the LCM and HCF of 403, 434 and 465.

Solution:

The relation between the LCM and HCF of 403, 434 and 465 is given as, HCF(403, 434, 465) = [(403 × 434 × 465) × LCM(403, 434, 465)]/[LCM(403, 434) × LCM (434, 465) × LCM(403, 465)]
⇒ Prime factorization of 403, 434 and 465:
- 403 = 13 × 31
- 434 = 2 × 7 × 31
- 465 = 3 × 5 × 31
∴ LCM of (403, 434), (434, 465), (403, 465), and (403, 434, 465) is 5642, 6510, 6045, and 84630 respectively.
Now, LHS = HCF(403, 434, 465) = 31.
And, RHS = [(403 × 434 × 465) × LCM(403, 434, 465)]/[LCM(403, 434) × LCM (434, 465) × LCM(403, 465)] = [(81329430) × 84630]/[5642 × 6510 × 6045]
LHS = RHS = 31.
Hence verified.

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FAQs on HCF of 403, 434 and 465

What is the HCF of 403, 434 and 465?

The HCF of 403, 434 and 465 is 31. To calculate the HCF of 403, 434 and 465, we need to factor each number (factors of 403 = 1, 13, 31, 403; factors of 434 = 1, 2, 7, 14, 31, 62, 217, 434; factors of 465 = 1, 3, 5, 15, 31, 93, 155, 465) and choose the highest factor that exactly divides 403, 434 and 465, i.e., 31.

How to Find the HCF of 403, 434 and 465 by Prime Factorization?

To find the HCF of 403, 434 and 465, we will find the prime factorization of given numbers, i.e. 403 = 13 × 31; 434 = 2 × 7 × 31; 465 = 3 × 5 × 31.
⇒ Since 31 is the only common prime factor of 403, 434 and 465. Hence, HCF(403, 434, 465) = 31.
☛ What is a Prime Number?

Which of the following is HCF of 403, 434 and 465? 31, 483, 514, 492, 509, 490, 488, 474

HCF of 403, 434, 465 will be the number that divides 403, 434, and 465 without leaving any remainder. The only number that satisfies the given condition is 31.

What is the Relation Between LCM and HCF of 403, 434 and 465?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 403, 434 and 465, i.e. HCF(403, 434, 465) = [(403 × 434 × 465) × LCM(403, 434, 465)]/[LCM(403, 434) × LCM (434, 465) × LCM(403, 465)].
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 403, 434 and 465?

There are three commonly used methods to find the HCF of 403, 434 and 465.

By Euclidean Algorithm
By Prime Factorization
By Long Division

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