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HCF of 170 and 238

HCF of 170 and 238 is the largest possible number that divides 170 and 238 exactly without any remainder. The factors of 170 and 238 are 1, 2, 5, 10, 17, 34, 85, 170 and 1, 2, 7, 14, 17, 34, 119, 238 respectively. There are 3 commonly used methods to find the HCF of 170 and 238 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 170 and 238
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 170 and 238?

Answer: HCF of 170 and 238 is 34.

Explanation:

The HCF of two non-zero integers, x(170) and y(238), is the highest positive integer m(34) that divides both x(170) and y(238) without any remainder.

Methods to Find HCF of 170 and 238

Let's look at the different methods for finding the HCF of 170 and 238.

Prime Factorization Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 170 and 238 by Prime Factorization

Prime factorization of 170 and 238 is (2 × 5 × 17) and (2 × 7 × 17) respectively. As visible, 170 and 238 have common prime factors. Hence, the HCF of 170 and 238 is 2 × 17 = 34.

HCF of 170 and 238 by Listing Common Factors

Factors of 170: 1, 2, 5, 10, 17, 34, 85, 170
Factors of 238: 1, 2, 7, 14, 17, 34, 119, 238

There are 4 common factors of 170 and 238, that are 1, 2, 34, and 17. Therefore, the highest common factor of 170 and 238 is 34.

HCF of 170 and 238 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 = 238 and Y = 170

HCF(238, 170) = HCF(170, 238 mod 170) = HCF(170, 68)
HCF(170, 68) = HCF(68, 170 mod 68) = HCF(68, 34)
HCF(68, 34) = HCF(34, 68 mod 34) = HCF(34, 0)
HCF(34, 0) = 34 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 170 and 238 is 34.

☛ Also Check:

HCF of 170 and 238 Examples

Example 1: The product of two numbers is 40460. If their HCF is 34, what is their LCM?

Solution:

Given: HCF = 34 and product of numbers = 40460
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 40460/34
Therefore, the LCM is 1190.
Example 2: Find the highest number that divides 170 and 238 exactly.

Solution:

The highest number that divides 170 and 238 exactly is their highest common factor, i.e. HCF of 170 and 238.
⇒ Factors of 170 and 238:
- Factors of 170 = 1, 2, 5, 10, 17, 34, 85, 170
- Factors of 238 = 1, 2, 7, 14, 17, 34, 119, 238
Therefore, the HCF of 170 and 238 is 34.
Example 3: Find the HCF of 170 and 238, if their LCM is 1190.

Solution:

∵ LCM × HCF = 170 × 238
⇒ HCF(170, 238) = (170 × 238)/1190 = 34
Therefore, the highest common factor of 170 and 238 is 34.

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FAQs on HCF of 170 and 238

What is the HCF of 170 and 238?

The HCF of 170 and 238 is 34. To calculate the HCF (Highest Common Factor) of 170 and 238, we need to factor each number (factors of 170 = 1, 2, 5, 10, 17, 34, 85, 170; factors of 238 = 1, 2, 7, 14, 17, 34, 119, 238) and choose the highest factor that exactly divides both 170 and 238, i.e., 34.

How to Find the HCF of 170 and 238 by Long Division Method?

To find the HCF of 170, 238 using long division method, 238 is divided by 170. The corresponding divisor (34) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 170 and 238?

There are three commonly used methods to find the HCF of 170 and 238.

By Long Division
By Prime Factorization
By Euclidean Algorithm

What is the Relation Between LCM and HCF of 170, 238?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 170 and 238, i.e. HCF × LCM = 170 × 238.

How to Find the HCF of 170 and 238 by Prime Factorization?

To find the HCF of 170 and 238, we will find the prime factorization of the given numbers, i.e. 170 = 2 × 5 × 17; 238 = 2 × 7 × 17.
⇒ Since 2, 17 are common terms in the prime factorization of 170 and 238. Hence, HCF(170, 238) = 2 × 17 = 34
☛ Prime Number

If the HCF of 238 and 170 is 34, Find its LCM.

HCF(238, 170) × LCM(238, 170) = 238 × 170
Since the HCF of 238 and 170 = 34
⇒ 34 × LCM(238, 170) = 40460
Therefore, LCM = 1190
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