HCF of 56 and 57

The HCF of 56 and 57 is 1. The Highest Common Factor is denoted as the largest number that divides the given numbers without leaving any remainder. Students who are facing difficulty in solving the problems of HCF can make use of the article Highest Common Factor to learn the simple techniques of calculating the HCF of the numbers effortlessly. This article also boosts skills in solving problems of HCF in a short span of time, which is vital from an exam perspective. Let us learn in detail how to find the Highest Common Factor of 56 and 57 using various methods in this article.

What is the HCF of 56 and 57?

The Highest Common Factor of 56 and 57 is 1. The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, and the factors of 57 are 1, 3, 19, 57. Clearly, 1 is the Highest Common Factor of 56 and 57.

How to Find HCF of 56 and 57?

There are three methods to find the HCF of 56 and 57:

• Prime Factorisation
• Long Division method
• Listing common factors

HCF of 56 and 57 by Prime Factorisation Method

In prime factorisation, given natural numbers are represented as the product of prime factors. Hence, 56 and 57 can be expressed as:

56 = 2 × 2 × 2 × 7

57 = 3 × 19

There is no common prime factor between 56 and 57.

Therefore,

HCF (56, 57) = 1

HCF of 56 and 57 by Long Division Method

In this method, to find the HCF of 56 and 57, we use the steps mentioned below:

Step 1: Divide the largest number by the smallest number from the given two numbers.

Step 2: Now, check the remainder. If it is not 0, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.

Step 3: Repeat this process until we get the remainder equal to zero. The last divisor will be the HCF of the given two numbers.

The Highest Common Factor of 56 and 57 by the long division method is as follows:

HCF (56, 57) = 1

HCF of 56 and 57 by Listing Common Factors

In this method, we list the factors of 56 and 57 and choose the largest of all the common factors. The factors of 56 and 57 are given below:

Factors of 56:1, 2, 4, 7, 8, 14, 28, 56

Factors of 57:1, 3, 19, 57

Hence, HCF (56, 57) = 1

Related Articles

• HCF of Two Numbers
• GCF
• HCF and LCM
• GCF Calculator
• HCF

Video Lesson on Properties of HCF and LCM

Solved Examples

1. What is the HCF of 56 and 57 if their LCM is 3192?

Solution: We know that

HCF × LCM = 56 × 57

Given 

LCM = 3192

HCF × 3192 = 56 × 57

HCF = 1

Therefore, the HCF of 56 and 57 is 1.

2. The HCF and LCM of two numbers are 1 and 3192. If one of the numbers is 57, what is the other number?

Solution: Let the other number be r.

HCF = 1

LCM = 3192

We know that

HCF × LCM = 57 × r

1 × 3192 = 57 × r

r = 56

Hence, the other number is 56.