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HCF of 56 and 57

HCF of 56 and 57 is the largest possible number that divides 56 and 57 exactly without any remainder. The factors of 56 and 57 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 3, 19, 57 respectively. There are 3 commonly used methods to find the HCF of 56 and 57 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 56 and 57
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 56 and 57?

Answer: HCF of 56 and 57 is 1.

Explanation:

The HCF of two non-zero integers, x(56) and y(57), is the highest positive integer m(1) that divides both x(56) and y(57) without any remainder.

Methods to Find HCF of 56 and 57

The methods to find the HCF of 56 and 57 are explained below.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

HCF of 56 and 57 by Long Division

HCF of 56 and 57 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 57 (larger number) by 56 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (56) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 56 and 57.

HCF of 56 and 57 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 = 57 and Y = 56

HCF(57, 56) = HCF(56, 57 mod 56) = HCF(56, 1)
HCF(56, 1) = HCF(1, 56 mod 1) = HCF(1, 0)
HCF(1, 0) = 1 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 56 and 57 is 1.

HCF of 56 and 57 by Prime Factorization

Prime factorization of 56 and 57 is (2 × 2 × 2 × 7) and (3 × 19) respectively. As visible, there are no common prime factors between 56 and 57, i.e. they are coprime. Hence, the HCF of 56 and 57 will be 1.

☛ Also Check:

HCF of 56 and 57 Examples

Example 1: Find the highest number that divides 56 and 57 exactly.

Solution:

The highest number that divides 56 and 57 exactly is their highest common factor, i.e. HCF of 56 and 57.
⇒ Factors of 56 and 57:
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 57 = 1, 3, 19, 57
Therefore, the HCF of 56 and 57 is 1.
Example 2: Find the HCF of 56 and 57, if their LCM is 3192.

Solution:

∵ LCM × HCF = 56 × 57
⇒ HCF(56, 57) = (56 × 57)/3192 = 1
Therefore, the highest common factor of 56 and 57 is 1.
Example 3: For two numbers, HCF = 1 and LCM = 3192. If one number is 57, find the other number.

Solution:

Given: HCF (y, 57) = 1 and LCM (y, 57) = 3192
∵ HCF × LCM = 57 × (y)
⇒ y = (HCF × LCM)/57
⇒ y = (1 × 3192)/57
⇒ y = 56
Therefore, the other number is 56.

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FAQs on HCF of 56 and 57

What is the HCF of 56 and 57?

The HCF of 56 and 57 is 1. To calculate the HCF of 56 and 57, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 57 = 1, 3, 19, 57) and choose the highest factor that exactly divides both 56 and 57, i.e., 1.

How to Find the HCF of 56 and 57 by Long Division Method?

To find the HCF of 56, 57 using long division method, 57 is divided by 56. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 56 and 57?

There are three commonly used methods to find the HCF of 56 and 57.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the HCF of 56 and 57 by Prime Factorization?

To find the HCF of 56 and 57, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 57 = 3 × 19.
⇒ There is no common prime factor for 56 and 57. Hence, HCF (56, 57) = 1.
☛ Prime Number

If the HCF of 57 and 56 is 1, Find its LCM.

HCF(57, 56) × LCM(57, 56) = 57 × 56
Since the HCF of 57 and 56 = 1
⇒ 1 × LCM(57, 56) = 3192
Therefore, LCM = 3192
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What is the Relation Between LCM and HCF of 56, 57?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 56 and 57, i.e. HCF × LCM = 56 × 57.

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