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HCF of 26 and 169

HCF of 26 and 169 is the largest possible number that divides 26 and 169 exactly without any remainder. The factors of 26 and 169 are 1, 2, 13, 26 and 1, 13, 169 respectively. There are 3 commonly used methods to find the HCF of 26 and 169 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 26 and 169
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 26 and 169?

Answer: HCF of 26 and 169 is 13.

Explanation:

The HCF of two non-zero integers, x(26) and y(169), is the highest positive integer m(13) that divides both x(26) and y(169) without any remainder.

Methods to Find HCF of 26 and 169

Let's look at the different methods for finding the HCF of 26 and 169.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

HCF of 26 and 169 by Long Division

HCF of 26 and 169 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 169 (larger number) by 26 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (26) by the remainder (13).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (13) is the HCF of 26 and 169.

HCF of 26 and 169 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 = 169 and Y = 26

HCF(169, 26) = HCF(26, 169 mod 26) = HCF(26, 13)
HCF(26, 13) = HCF(13, 26 mod 13) = HCF(13, 0)
HCF(13, 0) = 13 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 26 and 169 is 13.

HCF of 26 and 169 by Listing Common Factors

Factors of 26: 1, 2, 13, 26
Factors of 169: 1, 13, 169

There are 2 common factors of 26 and 169, that are 1 and 13. Therefore, the highest common factor of 26 and 169 is 13.

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HCF of 26 and 169 Examples

Example 1: The product of two numbers is 4394. If their HCF is 13, what is their LCM?

Solution:

Given: HCF = 13 and product of numbers = 4394
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 4394/13
Therefore, the LCM is 338.
Example 2: For two numbers, HCF = 13 and LCM = 338. If one number is 26, find the other number.

Solution:

Given: HCF (y, 26) = 13 and LCM (y, 26) = 338
∵ HCF × LCM = 26 × (y)
⇒ y = (HCF × LCM)/26
⇒ y = (13 × 338)/26
⇒ y = 169
Therefore, the other number is 169.
Example 3: Find the HCF of 26 and 169, if their LCM is 338.

Solution:

∵ LCM × HCF = 26 × 169
⇒ HCF(26, 169) = (26 × 169)/338 = 13
Therefore, the highest common factor of 26 and 169 is 13.

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FAQs on HCF of 26 and 169

What is the HCF of 26 and 169?

The HCF of 26 and 169 is 13. To calculate the Highest common factor (HCF) of 26 and 169, we need to factor each number (factors of 26 = 1, 2, 13, 26; factors of 169 = 1, 13, 169) and choose the highest factor that exactly divides both 26 and 169, i.e., 13.

How to Find the HCF of 26 and 169 by Prime Factorization?

To find the HCF of 26 and 169, we will find the prime factorization of the given numbers, i.e. 26 = 2 × 13; 169 = 13 × 13.
⇒ Since 13 is the only common prime factor of 26 and 169. Hence, HCF (26, 169) = 13.
☛ What is a Prime Number?

What are the Methods to Find HCF of 26 and 169?

There are three commonly used methods to find the HCF of 26 and 169.

By Prime Factorization
By Long Division
By Euclidean Algorithm

If the HCF of 169 and 26 is 13, Find its LCM.

HCF(169, 26) × LCM(169, 26) = 169 × 26
Since the HCF of 169 and 26 = 13
⇒ 13 × LCM(169, 26) = 4394
Therefore, LCM = 338
☛ Highest Common Factor Calculator

How to Find the HCF of 26 and 169 by Long Division Method?

To find the HCF of 26, 169 using long division method, 169 is divided by 26. The corresponding divisor (13) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 26, 169?

The following equation can be used to express the relation between Least Common Multiple and HCF of 26 and 169, i.e. HCF × LCM = 26 × 169.

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