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HCF of 28 and 32

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

1.	HCF of 28 and 32
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 28 and 32?

Answer: HCF of 28 and 32 is 4.

Explanation:

The HCF of two non-zero integers, x(28) and y(32), is the highest positive integer m(4) that divides both x(28) and y(32) without any remainder.

Methods to Find HCF of 28 and 32

Let's look at the different methods for finding the HCF of 28 and 32.

Listing Common Factors
Prime Factorization Method
Long Division Method

HCF of 28 and 32 by Listing Common Factors

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

There are 3 common factors of 28 and 32, that are 1, 2, and 4. Therefore, the highest common factor of 28 and 32 is 4.

HCF of 28 and 32 by Prime Factorization

Prime factorization of 28 and 32 is (2 × 2 × 7) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 28 and 32 have common prime factors. Hence, the HCF of 28 and 32 is 2 × 2 = 4.

HCF of 28 and 32 by Long Division

HCF of 28 and 32 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 32 (larger number) by 28 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 28 and 32.

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HCF of 28 and 32 Examples

Example 1: For two numbers, HCF = 4 and LCM = 224. If one number is 28, find the other number.

Solution:

Given: HCF (y, 28) = 4 and LCM (y, 28) = 224
∵ HCF × LCM = 28 × (y)
⇒ y = (HCF × LCM)/28
⇒ y = (4 × 224)/28
⇒ y = 32
Therefore, the other number is 32.
Example 2: The product of two numbers is 896. If their HCF is 4, what is their LCM?

Solution:

Given: HCF = 4 and product of numbers = 896
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 896/4
Therefore, the LCM is 224.
Example 3: Find the HCF of 28 and 32, if their LCM is 224.

Solution:

∵ LCM × HCF = 28 × 32
⇒ HCF(28, 32) = (28 × 32)/224 = 4
Therefore, the highest common factor of 28 and 32 is 4.

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FAQs on HCF of 28 and 32

What is the HCF of 28 and 32?

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

If the HCF of 32 and 28 is 4, Find its LCM.

HCF(32, 28) × LCM(32, 28) = 32 × 28
Since the HCF of 32 and 28 = 4
⇒ 4 × LCM(32, 28) = 896
Therefore, LCM = 224
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What is the Relation Between LCM and HCF of 28, 32?

The following equation can be used to express the relation between LCM and HCF of 28 and 32, i.e. HCF × LCM = 28 × 32.

How to Find the HCF of 28 and 32 by Prime Factorization?

To find the HCF of 28 and 32, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 28 and 32. Hence, HCF(28, 32) = 2 × 2 = 4
☛ What is a Prime Number?

What are the Methods to Find HCF of 28 and 32?

There are three commonly used methods to find the HCF of 28 and 32.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the HCF of 28 and 32 by Long Division Method?

To find the HCF of 28, 32 using long division method, 32 is divided by 28. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

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