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GCF of 61 and 73

GCF of 61 and 73 is the largest possible number that divides 61 and 73 exactly without any remainder. The factors of 61 and 73 are 1, 61 and 1, 73 respectively. There are 3 commonly used methods to find the GCF of 61 and 73 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 61 and 73
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 61 and 73?

Answer: GCF of 61 and 73 is 1.

Explanation:

The GCF of two non-zero integers, x(61) and y(73), is the greatest positive integer m(1) that divides both x(61) and y(73) without any remainder.

Methods to Find GCF of 61 and 73

Let's look at the different methods for finding the GCF of 61 and 73.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 61 and 73 by Listing Common Factors

Factors of 61: 1, 61
Factors of 73: 1, 73

Since, 1 is the only common factor between 61 and 73. The Greatest Common Factor of 61 and 73 is 1.

GCF of 61 and 73 by Long Division

GCF of 61 and 73 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 73 (larger number) by 61 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (61) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 61 and 73.

GCF of 61 and 73 by Prime Factorization

Prime factorization of 61 and 73 is (61) and (73) respectively. As visible, there are no common prime factors between 61 and 73, i.e. they are co-prime. Hence, the GCF of 61 and 73 will be 1.

☛ Also Check:

GCF of 61 and 73 Examples

Example 1: Find the GCF of 61 and 73, if their LCM is 4453.

Solution:

∵ LCM × GCF = 61 × 73
⇒ GCF(61, 73) = (61 × 73)/4453 = 1
Therefore, the greatest common factor of 61 and 73 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 4453. If one number is 73, find the other number.

Solution:

Given: GCF (y, 73) = 1 and LCM (y, 73) = 4453
∵ GCF × LCM = 73 × (y)
⇒ y = (GCF × LCM)/73
⇒ y = (1 × 4453)/73
⇒ y = 61
Therefore, the other number is 61.
Example 3: The product of two numbers is 4453. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 4453
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 4453/1
Therefore, the LCM is 4453.

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FAQs on GCF of 61 and 73

What is the GCF of 61 and 73?

The GCF of 61 and 73 is 1. To calculate the greatest common factor of 61 and 73, we need to factor each number (factors of 61 = 1, 61; factors of 73 = 1, 73) and choose the greatest factor that exactly divides both 61 and 73, i.e., 1.

How to Find the GCF of 61 and 73 by Long Division Method?

To find the GCF of 61, 73 using long division method, 73 is divided by 61. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

How to Find the GCF of 61 and 73 by Prime Factorization?

To find the GCF of 61 and 73, we will find the prime factorization of the given numbers, i.e. 61 = 61; 73 = 73.
⇒ There is no common prime factor for 61 and 73. Hence, GCF (61, 73) = 1.
☛ Prime Numbers

What is the Relation Between LCM and GCF of 61, 73?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 61 and 73, i.e. GCF × LCM = 61 × 73.

If the GCF of 73 and 61 is 1, Find its LCM.

GCF(73, 61) × LCM(73, 61) = 73 × 61
Since the GCF of 73 and 61 = 1
⇒ 1 × LCM(73, 61) = 4453
Therefore, LCM = 4453
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 61 and 73?

There are three commonly used methods to find the GCF of 61 and 73.

By Long Division
By Prime Factorization
By Euclidean Algorithm

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