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HCF of 26 and 91

HCF of 26 and 91 is the largest possible number that divides 26 and 91 exactly without any remainder. The factors of 26 and 91 are 1, 2, 13, 26 and 1, 7, 13, 91 respectively. There are 3 commonly used methods to find the HCF of 26 and 91 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 26 and 91
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 26 and 91?

Answer: HCF of 26 and 91 is 13.

Explanation:

The HCF of two non-zero integers, x(26) and y(91), is the highest positive integer m(13) that divides both x(26) and y(91) without any remainder.

Methods to Find HCF of 26 and 91

The methods to find the HCF of 26 and 91 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 26 and 91 by Long Division

HCF of 26 and 91 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 91 (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 91.

HCF of 26 and 91 by Listing Common Factors

Factors of 26: 1, 2, 13, 26
Factors of 91: 1, 7, 13, 91

There are 2 common factors of 26 and 91, that are 1 and 13. Therefore, the highest common factor of 26 and 91 is 13.

HCF of 26 and 91 by Prime Factorization

Prime factorization of 26 and 91 is (2 × 13) and (7 × 13) respectively. As visible, 26 and 91 have only one common prime factor i.e. 13. Hence, the HCF of 26 and 91 is 13.

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HCF of 26 and 91 Examples

Example 1: The product of two numbers is 2366. If their HCF is 13, what is their LCM?

Solution:

Given: HCF = 13 and product of numbers = 2366
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 2366/13
Therefore, the LCM is 182.
Example 2: Find the HCF of 26 and 91, if their LCM is 182.

Solution:

∵ LCM × HCF = 26 × 91
⇒ HCF(26, 91) = (26 × 91)/182 = 13
Therefore, the highest common factor of 26 and 91 is 13.
Example 3: Find the highest number that divides 26 and 91 exactly.

Solution:

The highest number that divides 26 and 91 exactly is their highest common factor, i.e. HCF of 26 and 91.
⇒ Factors of 26 and 91:
- Factors of 26 = 1, 2, 13, 26
- Factors of 91 = 1, 7, 13, 91
Therefore, the HCF of 26 and 91 is 13.

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FAQs on HCF of 26 and 91

What is the HCF of 26 and 91?

The HCF of 26 and 91 is 13. To calculate the Highest common factor (HCF) of 26 and 91, we need to factor each number (factors of 26 = 1, 2, 13, 26; factors of 91 = 1, 7, 13, 91) and choose the highest factor that exactly divides both 26 and 91, i.e., 13.

What are the Methods to Find HCF of 26 and 91?

There are three commonly used methods to find the HCF of 26 and 91.

By Prime Factorization
By Listing Common Factors
By Long Division

If the HCF of 91 and 26 is 13, Find its LCM.

HCF(91, 26) × LCM(91, 26) = 91 × 26
Since the HCF of 91 and 26 = 13
⇒ 13 × LCM(91, 26) = 2366
Therefore, LCM = 182
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How to Find the HCF of 26 and 91 by Prime Factorization?

To find the HCF of 26 and 91, we will find the prime factorization of the given numbers, i.e. 26 = 2 × 13; 91 = 7 × 13.
⇒ Since 13 is the only common prime factor of 26 and 91. Hence, HCF (26, 91) = 13.
☛ What is a Prime Number?

How to Find the HCF of 26 and 91 by Long Division Method?

To find the HCF of 26, 91 using long division method, 91 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, 91?

The following equation can be used to express the relation between LCM and HCF of 26 and 91, i.e. HCF × LCM = 26 × 91.

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