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HCF of 68 and 119

HCF of 68 and 119 is the largest possible number that divides 68 and 119 exactly without any remainder. The factors of 68 and 119 are 1, 2, 4, 17, 34, 68 and 1, 7, 17, 119 respectively. There are 3 commonly used methods to find the HCF of 68 and 119 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 68 and 119
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 68 and 119?

Answer: HCF of 68 and 119 is 17.

Explanation:

The HCF of two non-zero integers, x(68) and y(119), is the highest positive integer m(17) that divides both x(68) and y(119) without any remainder.

Methods to Find HCF of 68 and 119

The methods to find the HCF of 68 and 119 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 68 and 119 by Prime Factorization

Prime factorization of 68 and 119 is (2 × 2 × 17) and (7 × 17) respectively. As visible, 68 and 119 have only one common prime factor i.e. 17. Hence, the HCF of 68 and 119 is 17.

HCF of 68 and 119 by Long Division

HCF of 68 and 119 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 119 (larger number) by 68 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (68) by the remainder (51).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (17) is the HCF of 68 and 119.

HCF of 68 and 119 by Listing Common Factors

Factors of 68: 1, 2, 4, 17, 34, 68
Factors of 119: 1, 7, 17, 119

There are 2 common factors of 68 and 119, that are 1 and 17. Therefore, the highest common factor of 68 and 119 is 17.

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HCF of 68 and 119 Examples

Example 1: The product of two numbers is 8092. If their HCF is 17, what is their LCM?

Solution:

Given: HCF = 17 and product of numbers = 8092
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 8092/17
Therefore, the LCM is 476.
Example 2: Find the highest number that divides 68 and 119 exactly.

Solution:

The highest number that divides 68 and 119 exactly is their highest common factor, i.e. HCF of 68 and 119.
⇒ Factors of 68 and 119:
- Factors of 68 = 1, 2, 4, 17, 34, 68
- Factors of 119 = 1, 7, 17, 119
Therefore, the HCF of 68 and 119 is 17.
Example 3: For two numbers, HCF = 17 and LCM = 476. If one number is 119, find the other number.

Solution:

Given: HCF (y, 119) = 17 and LCM (y, 119) = 476
∵ HCF × LCM = 119 × (y)
⇒ y = (HCF × LCM)/119
⇒ y = (17 × 476)/119
⇒ y = 68
Therefore, the other number is 68.

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FAQs on HCF of 68 and 119

What is the HCF of 68 and 119?

The HCF of 68 and 119 is 17. To calculate the HCF (Highest Common Factor) of 68 and 119, we need to factor each number (factors of 68 = 1, 2, 4, 17, 34, 68; factors of 119 = 1, 7, 17, 119) and choose the highest factor that exactly divides both 68 and 119, i.e., 17.

How to Find the HCF of 68 and 119 by Long Division Method?

To find the HCF of 68, 119 using long division method, 119 is divided by 68. The corresponding divisor (17) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 68 and 119?

There are three commonly used methods to find the HCF of 68 and 119.

By Long Division
By Listing Common Factors
By Prime Factorization

If the HCF of 119 and 68 is 17, Find its LCM.

HCF(119, 68) × LCM(119, 68) = 119 × 68
Since the HCF of 119 and 68 = 17
⇒ 17 × LCM(119, 68) = 8092
Therefore, LCM = 476
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How to Find the HCF of 68 and 119 by Prime Factorization?

To find the HCF of 68 and 119, we will find the prime factorization of the given numbers, i.e. 68 = 2 × 2 × 17; 119 = 7 × 17.
⇒ Since 17 is the only common prime factor of 68 and 119. Hence, HCF (68, 119) = 17.
☛ What is a Prime Number?

What is the Relation Between LCM and HCF of 68, 119?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 68 and 119, i.e. HCF × LCM = 68 × 119.

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