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HCF of 391, 425 and 527

HCF of 391, 425 and 527 is the largest possible number that divides 391, 425 and 527 exactly without any remainder. The factors of 391, 425 and 527 are (1, 17, 23, 391), (1, 5, 17, 25, 85, 425) and (1, 17, 31, 527) respectively. There are 3 commonly used methods to find the HCF of 391, 425 and 527 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 391, 425 and 527
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 391, 425 and 527?

Answer: HCF of 391, 425 and 527 is 17.

Explanation:

The HCF of three non-zero integers, x(391), y(425) and z(527), is the highest positive integer m(17) that divides x(391), y(425) and z(527) without any remainder.

Methods to Find HCF of 391, 425 and 527

The methods to find the HCF of 391, 425 and 527 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

HCF of 391, 425 and 527 by Prime Factorization

Prime factorization of 391, 425 and 527 is (17 × 23), (5 × 5 × 17) and (17 × 31) respectively. As visible, 391, 425 and 527 have only one common prime factor i.e. 17. Hence, the HCF of 391, 425 and 527 is 17.

HCF of 391, 425 and 527 by Long Division

HCF of 391, 425 and 527 can be represented as HCF of (HCF of 391, 425) and 527. HCF(391, 425, 527) can be thus calculated by first finding HCF(391, 425) using long division and thereafter using this result with 527 to perform long division again.

Step 1: Divide 425 (larger number) by 391 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (391) by the remainder (34). Repeat this process until the remainder = 0.
⇒ HCF(391, 425) = 17.
Step 3: Now to find the HCF of 17 and 527, we will perform a long division on 527 and 17.
Step 4: For remainder = 0, divisor = 17 ⇒ HCF(17, 527) = 17

Thus, HCF(391, 425, 527) = HCF(HCF(391, 425), 527) = 17.

HCF of 391, 425 and 527 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(391, 425, 527) = HCF(HCF(391, 425), 527)

HCF(425, 391) = HCF(391, 425 mod 391) = HCF(391, 34)
HCF(391, 34) = HCF(34, 391 mod 34) = HCF(34, 17)
HCF(34, 17) = HCF(17, 34 mod 17) = HCF(17, 0)
HCF(17, 0) = 17 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(17, 527)

HCF(527, 17) = HCF(17, 527 mod 17) = HCF(17, 0)
HCF(17, 0) = 17 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 391, 425 and 527 is 17.

☛ Also Check:

HCF of 391, 425 and 527 Examples

Example 1: Find the highest number that divides 391, 425, and 527 completely.

Solution:

The highest number that divides 391, 425, and 527 exactly is their highest common factor.
- Factors of 391 = 1, 17, 23, 391
- Factors of 425 = 1, 5, 17, 25, 85, 425
- Factors of 527 = 1, 17, 31, 527
The HCF of 391, 425, and 527 is 17.
∴ The highest number that divides 391, 425, and 527 is 17.
Example 2: Verify the relation between the LCM and HCF of 391, 425 and 527.

Solution:

The relation between the LCM and HCF of 391, 425 and 527 is given as, HCF(391, 425, 527) = [(391 × 425 × 527) × LCM(391, 425, 527)]/[LCM(391, 425) × LCM (425, 527) × LCM(391, 527)]
⇒ Prime factorization of 391, 425 and 527:
- 391 = 17 × 23
- 425 = 5 × 5 × 17
- 527 = 17 × 31
∴ LCM of (391, 425), (425, 527), (391, 527), and (391, 425, 527) is 9775, 13175, 12121, and 303025 respectively.
Now, LHS = HCF(391, 425, 527) = 17.
And, RHS = [(391 × 425 × 527) × LCM(391, 425, 527)]/[LCM(391, 425) × LCM (425, 527) × LCM(391, 527)] = [(87574225) × 303025]/[9775 × 13175 × 12121]
LHS = RHS = 17.
Hence verified.
Example 3: Calculate the HCF of 391, 425, and 527 using LCM of the given numbers.

Solution:

Prime factorization of 391, 425 and 527 is given as,
- 391 = 17 × 23
- 425 = 5 × 5 × 17
- 527 = 17 × 31
LCM(391, 425) = 9775, LCM(425, 527) = 13175, LCM(527, 391) = 12121, LCM(391, 425, 527) = 303025
⇒ HCF(391, 425, 527) = [(391 × 425 × 527) × LCM(391, 425, 527)]/[LCM(391, 425) × LCM (425, 527) × LCM(527, 391)]
⇒ HCF(391, 425, 527) = (87574225 × 303025)/(9775 × 13175 × 12121)
⇒ HCF(391, 425, 527) = 17.
Therefore, the HCF of 391, 425 and 527 is 17.

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FAQs on HCF of 391, 425 and 527

What is the HCF of 391, 425 and 527?

The HCF of 391, 425 and 527 is 17. To calculate the highest common factor (HCF) of 391, 425 and 527, we need to factor each number (factors of 391 = 1, 17, 23, 391; factors of 425 = 1, 5, 17, 25, 85, 425; factors of 527 = 1, 17, 31, 527) and choose the highest factor that exactly divides 391, 425 and 527, i.e., 17.

What are the Methods to Find HCF of 391, 425 and 527?

There are three commonly used methods to find the HCF of 391, 425 and 527.

By Long Division
By Listing Common Factors
By Prime Factorization

Which of the following is HCF of 391, 425 and 527? 17, 528, 527, 567, 543, 533, 576, 547

HCF of 391, 425, 527 will be the number that divides 391, 425, and 527 without leaving any remainder. The only number that satisfies the given condition is 17.

What is the Relation Between LCM and HCF of 391, 425 and 527?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 391, 425 and 527, i.e. HCF(391, 425, 527) = [(391 × 425 × 527) × LCM(391, 425, 527)]/[LCM(391, 425) × LCM (425, 527) × LCM(391, 527)].
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How to Find the HCF of 391, 425 and 527 by Prime Factorization?

To find the HCF of 391, 425 and 527, we will find the prime factorization of given numbers, i.e. 391 = 17 × 23; 425 = 5 × 5 × 17; 527 = 17 × 31.
⇒ Since 17 is the only common prime factor of 391, 425 and 527. Hence, HCF(391, 425, 527) = 17.
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