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HCF of 16 and 24

HCF of 16 and 24 is the largest possible number that divides 16 and 24 exactly without any remainder. The factors of 16 and 24 are 1, 2, 4, 8, 16 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the HCF of 16 and 24 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 16 and 24
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 16 and 24?

Answer: HCF of 16 and 24 is 8.

Explanation:

The HCF of two non-zero integers, x(16) and y(24), is the highest positive integer m(8) that divides both x(16) and y(24) without any remainder.

Methods to Find HCF of 16 and 24

The methods to find the HCF of 16 and 24 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

HCF of 16 and 24 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 = 24 and Y = 16

HCF(24, 16) = HCF(16, 24 mod 16) = HCF(16, 8)
HCF(16, 8) = HCF(8, 16 mod 8) = HCF(8, 0)
HCF(8, 0) = 8 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 16 and 24 is 8.

HCF of 16 and 24 by Long Division

HCF of 16 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 24 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the HCF of 16 and 24.

HCF of 16 and 24 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

There are 4 common factors of 16 and 24, that are 8, 1, 2, and 4. Therefore, the highest common factor of 16 and 24 is 8.

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HCF of 16 and 24 Examples

Example 1: Find the HCF of 16 and 24, if their LCM is 48.

Solution:

∵ LCM × HCF = 16 × 24
⇒ HCF(16, 24) = (16 × 24)/48 = 8
Therefore, the highest common factor of 16 and 24 is 8.
Example 2: Find the highest number that divides 16 and 24 exactly.

Solution:

The highest number that divides 16 and 24 exactly is their highest common factor, i.e. HCF of 16 and 24.
⇒ Factors of 16 and 24:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the HCF of 16 and 24 is 8.
Example 3: The product of two numbers is 384. If their HCF is 8, what is their LCM?

Solution:

Given: HCF = 8 and product of numbers = 384
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 384/8
Therefore, the LCM is 48.

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FAQs on HCF of 16 and 24

What is the HCF of 16 and 24?

The HCF of 16 and 24 is 8. To calculate the Highest common factor (HCF) of 16 and 24, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the highest factor that exactly divides both 16 and 24, i.e., 8.

If the HCF of 24 and 16 is 8, Find its LCM.

HCF(24, 16) × LCM(24, 16) = 24 × 16
Since the HCF of 24 and 16 = 8
⇒ 8 × LCM(24, 16) = 384
Therefore, LCM = 48
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How to Find the HCF of 16 and 24 by Long Division Method?

To find the HCF of 16, 24 using long division method, 24 is divided by 16. The corresponding divisor (8) when remainder equals 0 is taken as HCF.

How to Find the HCF of 16 and 24 by Prime Factorization?

To find the HCF of 16 and 24, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 24 = 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 16 and 24. Hence, HCF(16, 24) = 2 × 2 × 2 = 8
☛ What is a Prime Number?

What is the Relation Between LCM and HCF of 16, 24?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 16 and 24, i.e. HCF × LCM = 16 × 24.

What are the Methods to Find HCF of 16 and 24?

There are three commonly used methods to find the HCF of 16 and 24.

By Prime Factorization
By Listing Common Factors
By Long Division

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