HCF of 26 and 91

HCF of 26 and 91 is 13. HCF or Highest Common Factor is the greatest number that divides two or more numbers. HCF is also known as Greatest Common Measure (GCM) or Greatest Common Divisor (GCD). Hence, we can say that GCF or GCD of 26 and 91 is 13.

In this article, we will learn how to HCF of 26 and 91 through Prime Factorization, listing factor, and long division method.

What is HCF of 26 and 91?

HCF of 26 and 91 is 13.

This implies 13 is the largest number which can evenly divide both 26 and 91 without leaving any remainder.

HCF of 26 and 91 Calculator

Try the following calculator to find the HCF of 26 and 91

How to find HCF of 26 and 91

Below are some of the methods of finding HCF of 26 and 91 by:

• Prime Factorization Method
• Listing Common Factors
• Long Division Method

HCF of 26 and 91 by Prime Factorization Method

Follow the below-given steps to find the HCF of numbers using the prime factorization method.

• Write each number as a product of prime factors. This method is called prime factorization.
• Now write the common factors of the two numbers
• The product of all common prime factors is the HCF

The prime factor of 26 and 91, respectively, are,

• 26 = 2 × 13
• 91 = 7 × 13

Since 13 is the largest and only common prime factor of 26 and 91

HCF(26, 91) = 13

HCF of 26 and 91 by Listing Common Factor

Listing Common Factor means identifying the numbers that can evenly divide two or more numbers.

By listing common factor of 26 and 91 we can start by listing the factors of each number:

• Factor of 26: 1, 2, 13, 26
• Factor of 91: 1, 7, 13, 91

Since 13 is the highest common factor among 26 and 91

Hence, HCF of 26 and 91 is 13

HCF of 26 and 91 by Long Division

Below are the steps for finding HCF of 26 and 91 by Long Division method:

• Divide the larger number by the smaller one.
• Replace the larger number with the smaller one and the smaller number with the Remainder.
• Repeat step 1 and 2 until we get a remainder of 0.

91 ÷ 26, Q = 3, R = 13

26 ÷ 13, Q = 2, R = 0

Therefore, HCF = 13

HCF and LCM of 26 and 91

Highest Common Factor or HCF of 26 and 91 is 13

Least Common Factor or LCM of 26 and 91 is 2 × 7 × 13 = 182.

Also, LCM × HCF = Product of Two Numbers

LCM × HCF = 182 × 13 = 2366

Product of 26 and 91 = 26 × 91 = 2366

Solved Example on HCF of 26 and 91

Below are some of the solved examples on HCF of 26 and 91

Example 1: If the product of two numbers = 2366 and HCF = 13, find the LCM?

Solution:

We know, LCM × HCF = product of numbers

LCM = Product/HCF = 2366/13

Therefore, the LCM is 182.

Example 2: Find the highest number that divides 26 and 91 exactly.

Solution:

The highest number that divides 26 and 91 exactly is their HCF.

26 = 2 × 13

91 = 7 × 13

HCF (26, 91) = 13

Example 3: For two numbers, HCF = 10 and LCM = 92. If one number is 92, find the other number.

Solution:

HCF × LCM = 92 × x

⇒ x = (HCF × LCM)/92

⇒ x = (10 × 92)/92

⇒ x = 10

Practice Problems on HCF of 26 and 91

Try out the following questions on HCF of 26 and 91

Q1. Find HCF of 94 and 18.

Q2. GCD and LCM of two numbers are 13 and 182 respectively. If one number is 26, find the other number.

Q3. Find LCM and HCF of 66 and 86.

Q4. The product of two numbers is 26382. If their HCF is 6, what is their LCM?

HCF of 26 and 91 FAQs

What is HCF of 26 and 91?

The HCF of 26 and 91 is 13.

What is the GCF of 26 and 91?

GCF or Greatest Common Factor of 26 and 91 is 13.

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

The methods used to find the LCM of 26 and 91 are:

• Prime Factorization Method
• Long Division Method
• Listing Common Factors

What is LCM of 26 and 91?

LCM of 26 and 91 is 182