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HCF of 82 and 104

HCF of 82 and 104 is the largest possible number that divides 82 and 104 exactly without any remainder. The factors of 82 and 104 are 1, 2, 41, 82 and 1, 2, 4, 8, 13, 26, 52, 104 respectively. There are 3 commonly used methods to find the HCF of 82 and 104 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 82 and 104
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 82 and 104?

Answer: HCF of 82 and 104 is 2.

Explanation:

The HCF of two non-zero integers, x(82) and y(104), is the highest positive integer m(2) that divides both x(82) and y(104) without any remainder.

Methods to Find HCF of 82 and 104

Let's look at the different methods for finding the HCF of 82 and 104.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

HCF of 82 and 104 by Long Division

HCF of 82 and 104 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 104 (larger number) by 82 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (82) by the remainder (22).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 82 and 104.

HCF of 82 and 104 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 = 104 and Y = 82

HCF(104, 82) = HCF(82, 104 mod 82) = HCF(82, 22)
HCF(82, 22) = HCF(22, 82 mod 22) = HCF(22, 16)
HCF(22, 16) = HCF(16, 22 mod 16) = HCF(16, 6)
HCF(16, 6) = HCF(6, 16 mod 6) = HCF(6, 4)
HCF(6, 4) = HCF(4, 6 mod 4) = HCF(4, 2)
HCF(4, 2) = HCF(2, 4 mod 2) = HCF(2, 0)
HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 82 and 104 is 2.

HCF of 82 and 104 by Prime Factorization

Prime factorization of 82 and 104 is (2 × 41) and (2 × 2 × 2 × 13) respectively. As visible, 82 and 104 have only one common prime factor i.e. 2. Hence, the HCF of 82 and 104 is 2.

☛ Also Check:

HCF of 82 and 104 Examples

Example 1: The product of two numbers is 8528. If their HCF is 2, what is their LCM?

Solution:

Given: HCF = 2 and product of numbers = 8528
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 8528/2
Therefore, the LCM is 4264.
Example 2: Find the highest number that divides 82 and 104 exactly.

Solution:

The highest number that divides 82 and 104 exactly is their highest common factor, i.e. HCF of 82 and 104.
⇒ Factors of 82 and 104:
- Factors of 82 = 1, 2, 41, 82
- Factors of 104 = 1, 2, 4, 8, 13, 26, 52, 104
Therefore, the HCF of 82 and 104 is 2.
Example 3: For two numbers, HCF = 2 and LCM = 4264. If one number is 82, find the other number.

Solution:

Given: HCF (y, 82) = 2 and LCM (y, 82) = 4264
∵ HCF × LCM = 82 × (y)
⇒ y = (HCF × LCM)/82
⇒ y = (2 × 4264)/82
⇒ y = 104
Therefore, the other number is 104.

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FAQs on HCF of 82 and 104

What is the HCF of 82 and 104?

The HCF of 82 and 104 is 2. To calculate the HCF of 82 and 104, we need to factor each number (factors of 82 = 1, 2, 41, 82; factors of 104 = 1, 2, 4, 8, 13, 26, 52, 104) and choose the highest factor that exactly divides both 82 and 104, i.e., 2.

What is the Relation Between LCM and HCF of 82, 104?

The following equation can be used to express the relation between LCM and HCF of 82 and 104, i.e. HCF × LCM = 82 × 104.

How to Find the HCF of 82 and 104 by Long Division Method?

To find the HCF of 82, 104 using long division method, 104 is divided by 82. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

How to Find the HCF of 82 and 104 by Prime Factorization?

To find the HCF of 82 and 104, we will find the prime factorization of the given numbers, i.e. 82 = 2 × 41; 104 = 2 × 2 × 2 × 13.
⇒ Since 2 is the only common prime factor of 82 and 104. Hence, HCF (82, 104) = 2.
☛ Prime Number

What are the Methods to Find HCF of 82 and 104?

There are three commonly used methods to find the HCF of 82 and 104.

By Long Division
By Prime Factorization
By Listing Common Factors

If the HCF of 104 and 82 is 2, Find its LCM.

HCF(104, 82) × LCM(104, 82) = 104 × 82
Since the HCF of 104 and 82 = 2
⇒ 2 × LCM(104, 82) = 8528
Therefore, LCM = 4264
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