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HCF of 34 and 85

HCF of 34 and 85 is the largest possible number that divides 34 and 85 exactly without any remainder. The factors of 34 and 85 are 1, 2, 17, 34 and 1, 5, 17, 85 respectively. There are 3 commonly used methods to find the HCF of 34 and 85 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 34 and 85
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 34 and 85?

Answer: HCF of 34 and 85 is 17.

Explanation:

The HCF of two non-zero integers, x(34) and y(85), is the highest positive integer m(17) that divides both x(34) and y(85) without any remainder.

Methods to Find HCF of 34 and 85

Let's look at the different methods for finding the HCF of 34 and 85.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 34 and 85 by Prime Factorization

Prime factorization of 34 and 85 is (2 × 17) and (5 × 17) respectively. As visible, 34 and 85 have only one common prime factor i.e. 17. Hence, the HCF of 34 and 85 is 17.

HCF of 34 and 85 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 = 85 and Y = 34

HCF(85, 34) = HCF(34, 85 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)

Therefore, the value of HCF of 34 and 85 is 17.

HCF of 34 and 85 by Listing Common Factors

Factors of 34: 1, 2, 17, 34
Factors of 85: 1, 5, 17, 85

There are 2 common factors of 34 and 85, that are 1 and 17. Therefore, the highest common factor of 34 and 85 is 17.

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HCF of 34 and 85 Examples

Example 1: Find the highest number that divides 34 and 85 exactly.

Solution:

The highest number that divides 34 and 85 exactly is their highest common factor, i.e. HCF of 34 and 85.
⇒ Factors of 34 and 85:
- Factors of 34 = 1, 2, 17, 34
- Factors of 85 = 1, 5, 17, 85
Therefore, the HCF of 34 and 85 is 17.
Example 2: Find the HCF of 34 and 85, if their LCM is 170.

Solution:

∵ LCM × HCF = 34 × 85
⇒ HCF(34, 85) = (34 × 85)/170 = 17
Therefore, the highest common factor of 34 and 85 is 17.
Example 3: The product of two numbers is 2890. If their HCF is 17, what is their LCM?

Solution:

Given: HCF = 17 and product of numbers = 2890
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 2890/17
Therefore, the LCM is 170.

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FAQs on HCF of 34 and 85

What is the HCF of 34 and 85?

The HCF of 34 and 85 is 17. To calculate the Highest common factor of 34 and 85, we need to factor each number (factors of 34 = 1, 2, 17, 34; factors of 85 = 1, 5, 17, 85) and choose the highest factor that exactly divides both 34 and 85, i.e., 17.

What are the Methods to Find HCF of 34 and 85?

There are three commonly used methods to find the HCF of 34 and 85.

By Long Division
By Euclidean Algorithm
By Prime Factorization

What is the Relation Between LCM and HCF of 34, 85?

The following equation can be used to express the relation between Least Common Multiple and HCF of 34 and 85, i.e. HCF × LCM = 34 × 85.

How to Find the HCF of 34 and 85 by Long Division Method?

To find the HCF of 34, 85 using long division method, 85 is divided by 34. The corresponding divisor (17) when remainder equals 0 is taken as HCF.

If the HCF of 85 and 34 is 17, Find its LCM.

HCF(85, 34) × LCM(85, 34) = 85 × 34
Since the HCF of 85 and 34 = 17
⇒ 17 × LCM(85, 34) = 2890
Therefore, LCM = 170
☛ Highest Common Factor Calculator

How to Find the HCF of 34 and 85 by Prime Factorization?

To find the HCF of 34 and 85, we will find the prime factorization of the given numbers, i.e. 34 = 2 × 17; 85 = 5 × 17.
⇒ Since 17 is the only common prime factor of 34 and 85. Hence, HCF (34, 85) = 17.
☛ Prime Number

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