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GCF of 45 and 60

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

1.	GCF of 45 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 45 and 60?

Answer: GCF of 45 and 60 is 15.

Explanation:

The GCF of two non-zero integers, x(45) and y(60), is the greatest positive integer m(15) that divides both x(45) and y(60) without any remainder.

Methods to Find GCF of 45 and 60

The methods to find the GCF of 45 and 60 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 45 and 60 by Long Division

GCF of 45 and 60 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 60 (larger number) by 45 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (45) by the remainder (15).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (15) is the GCF of 45 and 60.

GCF of 45 and 60 by Prime Factorization

Prime factorization of 45 and 60 is (3 × 3 × 5) and (2 × 2 × 3 × 5) respectively. As visible, 45 and 60 have common prime factors. Hence, the GCF of 45 and 60 is 3 × 5 = 15.

GCF of 45 and 60 by Listing Common Factors

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

There are 4 common factors of 45 and 60, that are 1, 3, 5, and 15. Therefore, the greatest common factor of 45 and 60 is 15.

☛ Also Check:

GCF of 45 and 60 Examples

Example 1: The product of two numbers is 2700. If their GCF is 15, what is their LCM?

Solution:

Given: GCF = 15 and product of numbers = 2700
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2700/15
Therefore, the LCM is 180.
Example 2: For two numbers, GCF = 15 and LCM = 180. If one number is 45, find the other number.

Solution:

Given: GCF (x, 45) = 15 and LCM (x, 45) = 180
∵ GCF × LCM = 45 × (x)
⇒ x = (GCF × LCM)/45
⇒ x = (15 × 180)/45
⇒ x = 60
Therefore, the other number is 60.
Example 3: Find the greatest number that divides 45 and 60 exactly.

Solution:

The greatest number that divides 45 and 60 exactly is their greatest common factor, i.e. GCF of 45 and 60.
⇒ Factors of 45 and 60:
- Factors of 45 = 1, 3, 5, 9, 15, 45
- Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Therefore, the GCF of 45 and 60 is 15.

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FAQs on GCF of 45 and 60

What is the GCF of 45 and 60?

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

How to Find the GCF of 45 and 60 by Prime Factorization?

To find the GCF of 45 and 60, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 60 = 2 × 2 × 3 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 45 and 60. Hence, GCF(45, 60) = 3 × 5 = 15
☛ Prime Number

What is the Relation Between LCM and GCF of 45, 60?

The following equation can be used to express the relation between Least Common Multiple and GCF of 45 and 60, i.e. GCF × LCM = 45 × 60.

If the GCF of 60 and 45 is 15, Find its LCM.

GCF(60, 45) × LCM(60, 45) = 60 × 45
Since the GCF of 60 and 45 = 15
⇒ 15 × LCM(60, 45) = 2700
Therefore, LCM = 180
☛ Greatest Common Factor Calculator

How to Find the GCF of 45 and 60 by Long Division Method?

To find the GCF of 45, 60 using long division method, 60 is divided by 45. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 45 and 60?

There are three commonly used methods to find the GCF of 45 and 60.

By Euclidean Algorithm
By Prime Factorization
By Long Division

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