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HCF of 56 and 88

HCF of 56 and 88 is the largest possible number that divides 56 and 88 exactly without any remainder. The factors of 56 and 88 are 1, 2, 4, 7, 8, 14, 28, 56 and 1, 2, 4, 8, 11, 22, 44, 88 respectively. There are 3 commonly used methods to find the HCF of 56 and 88 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 56 and 88
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 56 and 88?

Answer: HCF of 56 and 88 is 8.

Explanation:

The HCF of two non-zero integers, x(56) and y(88), is the highest positive integer m(8) that divides both x(56) and y(88) without any remainder.

Methods to Find HCF of 56 and 88

Let's look at the different methods for finding the HCF of 56 and 88.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

HCF of 56 and 88 by Listing Common Factors

Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88

There are 4 common factors of 56 and 88, that are 8, 1, 2, and 4. Therefore, the highest common factor of 56 and 88 is 8.

HCF of 56 and 88 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 = 88 and Y = 56

HCF(88, 56) = HCF(56, 88 mod 56) = HCF(56, 32)
HCF(56, 32) = HCF(32, 56 mod 32) = HCF(32, 24)
HCF(32, 24) = HCF(24, 32 mod 24) = HCF(24, 8)
HCF(24, 8) = HCF(8, 24 mod 8) = HCF(8, 0)
HCF(8, 0) = 8 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 56 and 88 is 8.

HCF of 56 and 88 by Long Division

HCF of 56 and 88 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 88 (larger number) by 56 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (56) by the remainder (32).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the HCF of 56 and 88.

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HCF of 56 and 88 Examples

Example 1: The product of two numbers is 4928. If their HCF is 8, what is their LCM?

Solution:

Given: HCF = 8 and product of numbers = 4928
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 4928/8
Therefore, the LCM is 616.
Example 2: Find the HCF of 56 and 88, if their LCM is 616.

Solution:

∵ LCM × HCF = 56 × 88
⇒ HCF(56, 88) = (56 × 88)/616 = 8
Therefore, the highest common factor of 56 and 88 is 8.
Example 3: For two numbers, HCF = 8 and LCM = 616. If one number is 88, find the other number.

Solution:

Given: HCF (y, 88) = 8 and LCM (y, 88) = 616
∵ HCF × LCM = 88 × (y)
⇒ y = (HCF × LCM)/88
⇒ y = (8 × 616)/88
⇒ y = 56
Therefore, the other number is 56.

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FAQs on HCF of 56 and 88

What is the HCF of 56 and 88?

The HCF of 56 and 88 is 8. To calculate the Highest common factor of 56 and 88, we need to factor each number (factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56; factors of 88 = 1, 2, 4, 8, 11, 22, 44, 88) and choose the highest factor that exactly divides both 56 and 88, i.e., 8.

What are the Methods to Find HCF of 56 and 88?

There are three commonly used methods to find the HCF of 56 and 88.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the HCF of 56 and 88 by Long Division Method?

To find the HCF of 56, 88 using long division method, 88 is divided by 56. The corresponding divisor (8) when remainder equals 0 is taken as HCF.

If the HCF of 88 and 56 is 8, Find its LCM.

HCF(88, 56) × LCM(88, 56) = 88 × 56
Since the HCF of 88 and 56 = 8
⇒ 8 × LCM(88, 56) = 4928
Therefore, LCM = 616
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What is the Relation Between LCM and HCF of 56, 88?

The following equation can be used to express the relation between LCM and HCF of 56 and 88, i.e. HCF × LCM = 56 × 88.

How to Find the HCF of 56 and 88 by Prime Factorization?

To find the HCF of 56 and 88, we will find the prime factorization of the given numbers, i.e. 56 = 2 × 2 × 2 × 7; 88 = 2 × 2 × 2 × 11.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 56 and 88. Hence, HCF(56, 88) = 2 × 2 × 2 = 8
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