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GCF of 45 and 120

GCF of 45 and 120 is the largest possible number that divides 45 and 120 exactly without any remainder. The factors of 45 and 120 are 1, 3, 5, 9, 15, 45 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 respectively. There are 3 commonly used methods to find the GCF of 45 and 120 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 45 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 45 and 120?

Answer: GCF of 45 and 120 is 15.

Explanation:

The GCF of two non-zero integers, x(45) and y(120), is the greatest positive integer m(15) that divides both x(45) and y(120) without any remainder.

Methods to Find GCF of 45 and 120

The methods to find the GCF of 45 and 120 are explained below.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 45 and 120 by Long Division

GCF of 45 and 120 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 120 (larger number) by 45 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (45) by the remainder (30).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (15) is the GCF of 45 and 120.

GCF of 45 and 120 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 = 120 and Y = 45

GCF(120, 45) = GCF(45, 120 mod 45) = GCF(45, 30)
GCF(45, 30) = GCF(30, 45 mod 30) = GCF(30, 15)
GCF(30, 15) = GCF(15, 30 mod 15) = GCF(15, 0)
GCF(15, 0) = 15 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 45 and 120 is 15.

GCF of 45 and 120 by Listing Common Factors

Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

There are 4 common factors of 45 and 120, that are 1, 3, 5, and 15. Therefore, the greatest common factor of 45 and 120 is 15.

☛ Also Check:

GCF of 45 and 120 Examples

Example 1: Find the greatest number that divides 45 and 120 exactly.

Solution:

The greatest number that divides 45 and 120 exactly is their greatest common factor, i.e. GCF of 45 and 120.
⇒ Factors of 45 and 120:
- Factors of 45 = 1, 3, 5, 9, 15, 45
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Therefore, the GCF of 45 and 120 is 15.
Example 2: For two numbers, GCF = 15 and LCM = 360. If one number is 45, find the other number.

Solution:

Given: GCF (x, 45) = 15 and LCM (x, 45) = 360
∵ GCF × LCM = 45 × (x)
⇒ x = (GCF × LCM)/45
⇒ x = (15 × 360)/45
⇒ x = 120
Therefore, the other number is 120.
Example 3: The product of two numbers is 5400. If their GCF is 15, what is their LCM?

Solution:

Given: GCF = 15 and product of numbers = 5400
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 5400/15
Therefore, the LCM is 360.

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FAQs on GCF of 45 and 120

What is the GCF of 45 and 120?

The GCF of 45 and 120 is 15. To calculate the greatest common factor (GCF) of 45 and 120, we need to factor each number (factors of 45 = 1, 3, 5, 9, 15, 45; factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and choose the greatest factor that exactly divides both 45 and 120, i.e., 15.

How to Find the GCF of 45 and 120 by Prime Factorization?

To find the GCF of 45 and 120, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 45 and 120. Hence, GCF(45, 120) = 3 × 5 = 15
☛ What is a Prime Number?

If the GCF of 120 and 45 is 15, Find its LCM.

GCF(120, 45) × LCM(120, 45) = 120 × 45
Since the GCF of 120 and 45 = 15
⇒ 15 × LCM(120, 45) = 5400
Therefore, LCM = 360
☛ GCF Calculator

How to Find the GCF of 45 and 120 by Long Division Method?

To find the GCF of 45, 120 using long division method, 120 is divided by 45. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 45, 120?

The following equation can be used to express the relation between Least Common Multiple and GCF of 45 and 120, i.e. GCF × LCM = 45 × 120.

What are the Methods to Find GCF of 45 and 120?

There are three commonly used methods to find the GCF of 45 and 120.

By Euclidean Algorithm
By Long Division
By Prime Factorization

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