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HCF of 32 and 56

HCF of 32 and 56 is the largest possible number that divides 32 and 56 exactly without any remainder. The factors of 32 and 56 are 1, 2, 4, 8, 16, 32 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 commonly used methods to find the HCF of 32 and 56 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 32 and 56
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 32 and 56?

Answer: HCF of 32 and 56 is 8.

Explanation:

The HCF of two non-zero integers, x(32) and y(56), is the highest positive integer m(8) that divides both x(32) and y(56) without any remainder.

Methods to Find HCF of 32 and 56

The methods to find the HCF of 32 and 56 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 32 and 56 by Prime Factorization

Prime factorization of 32 and 56 is (2 × 2 × 2 × 2 × 2) and (2 × 2 × 2 × 7) respectively. As visible, 32 and 56 have common prime factors. Hence, the HCF of 32 and 56 is 2 × 2 × 2 = 8.

HCF of 32 and 56 by Long Division

HCF of 32 and 56 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 56 (larger number) by 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (24).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the HCF of 32 and 56.

HCF of 32 and 56 by Listing Common Factors

Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56

There are 4 common factors of 32 and 56, that are 8, 1, 2, and 4. Therefore, the highest common factor of 32 and 56 is 8.

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HCF of 32 and 56 Examples

Example 1: For two numbers, HCF = 8 and LCM = 224. If one number is 32, find the other number.

Solution:

Given: HCF (y, 32) = 8 and LCM (y, 32) = 224
∵ HCF × LCM = 32 × (y)
⇒ y = (HCF × LCM)/32
⇒ y = (8 × 224)/32
⇒ y = 56
Therefore, the other number is 56.
Example 2: The product of two numbers is 1792. If their HCF is 8, what is their LCM?

Solution:

Given: HCF = 8 and product of numbers = 1792
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1792/8
Therefore, the LCM is 224.
Example 3: Find the HCF of 32 and 56, if their LCM is 224.

Solution:

∵ LCM × HCF = 32 × 56
⇒ HCF(32, 56) = (32 × 56)/224 = 8
Therefore, the highest common factor of 32 and 56 is 8.

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FAQs on HCF of 32 and 56

What is the HCF of 32 and 56?

The HCF of 32 and 56 is 8. To calculate the HCF (Highest Common Factor) of 32 and 56, we need to factor each number (factors of 32 = 1, 2, 4, 8, 16, 32; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56) and choose the highest factor that exactly divides both 32 and 56, i.e., 8.

What is the Relation Between LCM and HCF of 32, 56?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 32 and 56, i.e. HCF × LCM = 32 × 56.

How to Find the HCF of 32 and 56 by Prime Factorization?

To find the HCF of 32 and 56, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 56 = 2 × 2 × 2 × 7.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 32 and 56. Hence, HCF(32, 56) = 2 × 2 × 2 = 8
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What are the Methods to Find HCF of 32 and 56?

There are three commonly used methods to find the HCF of 32 and 56.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the HCF of 32 and 56 by Long Division Method?

To find the HCF of 32, 56 using long division method, 56 is divided by 32. The corresponding divisor (8) when remainder equals 0 is taken as HCF.

If the HCF of 56 and 32 is 8, Find its LCM.

HCF(56, 32) × LCM(56, 32) = 56 × 32
Since the HCF of 56 and 32 = 8
⇒ 8 × LCM(56, 32) = 1792
Therefore, LCM = 224
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