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GCF of 5 and 7

GCF of 5 and 7 is the largest possible number that divides 5 and 7 exactly without any remainder. The factors of 5 and 7 are 1, 5 and 1, 7 respectively. There are 3 commonly used methods to find the GCF of 5 and 7 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 5 and 7
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 5 and 7?

Answer: GCF of 5 and 7 is 1.

Explanation:

The GCF of two non-zero integers, x(5) and y(7), is the greatest positive integer m(1) that divides both x(5) and y(7) without any remainder.

Methods to Find GCF of 5 and 7

Let's look at the different methods for finding the GCF of 5 and 7.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 5 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 = 5

GCF(7, 5) = GCF(5, 7 mod 5) = GCF(5, 2)
GCF(5, 2) = GCF(2, 5 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 5 and 7 is 1.

GCF of 5 and 7 by Prime Factorization

Prime factorization of 5 and 7 is (5) and (7) respectively. As visible, there are no common prime factors between 5 and 7, i.e. they are coprime. Hence, the GCF of 5 and 7 will be 1.

GCF of 5 and 7 by Long Division

GCF of 5 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 5 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (5) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 5 and 7.

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GCF of 5 and 7 Examples

Example 1: The product of two numbers is 35. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 35
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 35/1
Therefore, the LCM is 35.
Example 2: For two numbers, GCF = 1 and LCM = 35. If one number is 5, find the other number.

Solution:

Given: GCF (x, 5) = 1 and LCM (x, 5) = 35
∵ GCF × LCM = 5 × (x)
⇒ x = (GCF × LCM)/5
⇒ x = (1 × 35)/5
⇒ x = 7
Therefore, the other number is 7.
Example 3: Find the greatest number that divides 5 and 7 exactly.

Solution:

The greatest number that divides 5 and 7 exactly is their greatest common factor, i.e. GCF of 5 and 7.
⇒ Factors of 5 and 7:
- Factors of 5 = 1, 5
- Factors of 7 = 1, 7
Therefore, the GCF of 5 and 7 is 1.

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FAQs on GCF of 5 and 7

What is the GCF of 5 and 7?

The GCF of 5 and 7 is 1. To calculate the greatest common factor (GCF) of 5 and 7, we need to factor each number (factors of 5 = 1, 5; factors of 7 = 1, 7) and choose the greatest factor that exactly divides both 5 and 7, i.e., 1.

What are the Methods to Find GCF of 5 and 7?

There are three commonly used methods to find the GCF of 5 and 7.

By Long Division
By Prime Factorization
By Listing Common Factors

If the GCF of 7 and 5 is 1, Find its LCM.

GCF(7, 5) × LCM(7, 5) = 7 × 5
Since the GCF of 7 and 5 = 1
⇒ 1 × LCM(7, 5) = 35
Therefore, LCM = 35
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What is the Relation Between LCM and GCF of 5, 7?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 5 and 7, i.e. GCF × LCM = 5 × 7.

How to Find the GCF of 5 and 7 by Long Division Method?

To find the GCF of 5, 7 using long division method, 7 is divided by 5. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

How to Find the GCF of 5 and 7 by Prime Factorization?

To find the GCF of 5 and 7, we will find the prime factorization of the given numbers, i.e. 5 = 5; 7 = 7.
⇒ There is no common prime factor for 5 and 7. Hence, GCF (5, 7) = 1.
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