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GCF of 32 and 45

GCF of 32 and 45 is the largest possible number that divides 32 and 45 exactly without any remainder. The factors of 32 and 45 are 1, 2, 4, 8, 16, 32 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used methods to find the GCF of 32 and 45 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 32 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 32 and 45?

Answer: GCF of 32 and 45 is 1.

Explanation:

The GCF of two non-zero integers, x(32) and y(45), is the greatest positive integer m(1) that divides both x(32) and y(45) without any remainder.

Methods to Find GCF of 32 and 45

The methods to find the GCF of 32 and 45 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 32 and 45 by Prime Factorization

Prime factorization of 32 and 45 is (2 × 2 × 2 × 2 × 2) and (3 × 3 × 5) respectively. As visible, there are no common prime factors between 32 and 45, i.e. they are coprime. Hence, the GCF of 32 and 45 will be 1.

GCF of 32 and 45 by Listing Common Factors

Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 45: 1, 3, 5, 9, 15, 45

Since, 1 is the only common factor between 32 and 45. The Greatest Common Factor of 32 and 45 is 1.

GCF of 32 and 45 by Long Division

GCF of 32 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (13).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 32 and 45.

☛ Also Check:

GCF of 32 and 45 Examples

Example 1: Find the GCF of 32 and 45, if their LCM is 1440.

Solution:

∵ LCM × GCF = 32 × 45
⇒ GCF(32, 45) = (32 × 45)/1440 = 1
Therefore, the greatest common factor of 32 and 45 is 1.
Example 2: The product of two numbers is 1440. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 1440
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1440/1
Therefore, the LCM is 1440.
Example 3: For two numbers, GCF = 1 and LCM = 1440. If one number is 45, find the other number.

Solution:

Given: GCF (y, 45) = 1 and LCM (y, 45) = 1440
∵ GCF × LCM = 45 × (y)
⇒ y = (GCF × LCM)/45
⇒ y = (1 × 1440)/45
⇒ y = 32
Therefore, the other number is 32.

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FAQs on GCF of 32 and 45

What is the GCF of 32 and 45?

The GCF of 32 and 45 is 1. To calculate the greatest common factor (GCF) of 32 and 45, we need to factor each number (factors of 32 = 1, 2, 4, 8, 16, 32; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 32 and 45, i.e., 1.

How to Find the GCF of 32 and 45 by Long Division Method?

To find the GCF of 32, 45 using long division method, 45 is divided by 32. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 32, 45?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 32 and 45, i.e. GCF × LCM = 32 × 45.

What are the Methods to Find GCF of 32 and 45?

There are three commonly used methods to find the GCF of 32 and 45.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 32 and 45 by Prime Factorization?

To find the GCF of 32 and 45, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 45 = 3 × 3 × 5.
⇒ There is no common prime factor for 32 and 45. Hence, GCF (32, 45) = 1.
☛ What are Prime Numbers?

If the GCF of 45 and 32 is 1, Find its LCM.

GCF(45, 32) × LCM(45, 32) = 45 × 32
Since the GCF of 45 and 32 = 1
⇒ 1 × LCM(45, 32) = 1440
Therefore, LCM = 1440
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