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GCF of 24 and 100

GCF of 24 and 100 is the largest possible number that divides 24 and 100 exactly without any remainder. The factors of 24 and 100 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 24 and 100 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 24 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 100?

Answer: GCF of 24 and 100 is 4.

Explanation:

The GCF of two non-zero integers, x(24) and y(100), is the greatest positive integer m(4) that divides both x(24) and y(100) without any remainder.

Methods to Find GCF of 24 and 100

The methods to find the GCF of 24 and 100 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 24 and 100 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 100 and Y = 24

GCF(100, 24) = GCF(24, 100 mod 24) = GCF(24, 4)
GCF(24, 4) = GCF(4, 24 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 24 and 100 is 4.

GCF of 24 and 100 by Long Division

GCF of 24 and 100 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 100 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 24 and 100.

GCF of 24 and 100 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 3 common factors of 24 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 24 and 100 is 4.

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GCF of 24 and 100 Examples

Example 1: For two numbers, GCF = 4 and LCM = 600. If one number is 24, find the other number.

Solution:

Given: GCF (x, 24) = 4 and LCM (x, 24) = 600
∵ GCF × LCM = 24 × (x)
⇒ x = (GCF × LCM)/24
⇒ x = (4 × 600)/24
⇒ x = 100
Therefore, the other number is 100.
Example 2: The product of two numbers is 2400. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 2400
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2400/4
Therefore, the LCM is 600.
Example 3: Find the GCF of 24 and 100, if their LCM is 600.

Solution:

∵ LCM × GCF = 24 × 100
⇒ GCF(24, 100) = (24 × 100)/600 = 4
Therefore, the greatest common factor of 24 and 100 is 4.

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FAQs on GCF of 24 and 100

What is the GCF of 24 and 100?

The GCF of 24 and 100 is 4. To calculate the greatest common factor (GCF) of 24 and 100, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 24 and 100, i.e., 4.

If the GCF of 100 and 24 is 4, Find its LCM.

GCF(100, 24) × LCM(100, 24) = 100 × 24
Since the GCF of 100 and 24 = 4
⇒ 4 × LCM(100, 24) = 2400
Therefore, LCM = 600
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How to Find the GCF of 24 and 100 by Long Division Method?

To find the GCF of 24, 100 using long division method, 100 is divided by 24. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 24, 100?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 24 and 100, i.e. GCF × LCM = 24 × 100.

What are the Methods to Find GCF of 24 and 100?

There are three commonly used methods to find the GCF of 24 and 100.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 24 and 100 by Prime Factorization?

To find the GCF of 24 and 100, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 100 = 2 × 2 × 5 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 24 and 100. Hence, GCF(24, 100) = 2 × 2 = 4
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