GCF of 5 and 7 | How to Find GCF of 5, 7? (2024)

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.

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.

☛ Also Check:

GCF of 28 and 35 = 7
GCF of 24 and 56 = 8
GCF of 84 and 90 = 6
GCF of 3 and 9 = 3
GCF of 9 and 24 = 3
GCF of 12 and 72 = 12
GCF of 16 and 32 = 16

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.
See Also
Factors of 8 | How to Find the Prime Factors of 8 | Examples
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
☛ GCF Calculator

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.
☛ Prime Numbers