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GCF of 3 and 7

GCF of 3 and 7 is the largest possible number that divides 3 and 7 exactly without any remainder. The factors of 3 and 7 are 1, 3 and 1, 7 respectively. There are 3 commonly used methods to find the GCF of 3 and 7 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 3 and 7
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 3 and 7?

Answer: GCF of 3 and 7 is 1.

Explanation:

The GCF of two non-zero integers, x(3) and y(7), is the greatest positive integer m(1) that divides both x(3) and y(7) without any remainder.

Methods to Find GCF of 3 and 7

Let's look at the different methods for finding the GCF of 3 and 7.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

GCF of 3 and 7 by Listing Common Factors

Factors of 3: 1, 3
Factors of 7: 1, 7

Since, 1 is the only common factor between 3 and 7. The Greatest Common Factor of 3 and 7 is 1.

GCF of 3 and 7 by Long Division

GCF of 3 and 7 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 7 (larger number) by 3 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (3) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 3 and 7.

GCF of 3 and 7 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 = 7 and Y = 3

GCF(7, 3) = GCF(3, 7 mod 3) = GCF(3, 1)
GCF(3, 1) = GCF(1, 3 mod 1) = GCF(1, 0)
GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 3 and 7 is 1.

☛ Also Check:

GCF of 3 and 7 Examples

Example 1: Find the GCF of 3 and 7, if their LCM is 21.

Solution:

∵ LCM × GCF = 3 × 7
⇒ GCF(3, 7) = (3 × 7)/21 = 1
Therefore, the greatest common factor of 3 and 7 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 21. If one number is 3, find the other number.

Solution:

Given: GCF (z, 3) = 1 and LCM (z, 3) = 21
∵ GCF × LCM = 3 × (z)
⇒ z = (GCF × LCM)/3
⇒ z = (1 × 21)/3
⇒ z = 7
Therefore, the other number is 7.
Example 3: The product of two numbers is 21. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 21
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 21/1
Therefore, the LCM is 21.

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FAQs on GCF of 3 and 7

What is the GCF of 3 and 7?

The GCF of 3 and 7 is 1. To calculate the GCF of 3 and 7, we need to factor each number (factors of 3 = 1, 3; factors of 7 = 1, 7) and choose the greatest factor that exactly divides both 3 and 7, i.e., 1.

If the GCF of 7 and 3 is 1, Find its LCM.

GCF(7, 3) × LCM(7, 3) = 7 × 3
Since the GCF of 7 and 3 = 1
⇒ 1 × LCM(7, 3) = 21
Therefore, LCM = 21
☛ Greatest Common Factor Calculator

How to Find the GCF of 3 and 7 by Prime Factorization?

To find the GCF of 3 and 7, we will find the prime factorization of the given numbers, i.e. 3 = 3; 7 = 7.
⇒ There is no common prime factor for 3 and 7. Hence, GCF (3, 7) = 1.
☛ Prime Numbers

What is the Relation Between LCM and GCF of 3, 7?

The following equation can be used to express the relation between LCM and GCF of 3 and 7, i.e. GCF × LCM = 3 × 7.

What are the Methods to Find GCF of 3 and 7?

There are three commonly used methods to find the GCF of 3 and 7.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 3 and 7 by Long Division Method?

To find the GCF of 3, 7 using long division method, 7 is divided by 3. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

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