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GCF of 7 and 56

GCF of 7 and 56 is the largest possible number that divides 7 and 56 exactly without any remainder. The factors of 7 and 56 are 1, 7 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 commonly used methods to find the GCF of 7 and 56 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 7 and 56
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 7 and 56?

Answer: GCF of 7 and 56 is 7.

Explanation:

The GCF of two non-zero integers, x(7) and y(56), is the greatest positive integer m(7) that divides both x(7) and y(56) without any remainder.

Methods to Find GCF of 7 and 56

The methods to find the GCF of 7 and 56 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 7 and 56 by Prime Factorization

Prime factorization of 7 and 56 is (7) and (2 × 2 × 2 × 7) respectively. As visible, 7 and 56 have only one common prime factor i.e. 7. Hence, the GCF of 7 and 56 is 7.

GCF of 7 and 56 by Long Division

GCF of 7 and 56 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 56 (larger number) by 7 (smaller number).
Step 2: Since the remainder = 0, the divisor (7) is the GCF of 7 and 56.

The corresponding divisor (7) is the GCF of 7 and 56.

GCF of 7 and 56 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 = 56 and Y = 7

GCF(56, 7) = GCF(7, 56 mod 7) = GCF(7, 0)
GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 7 and 56 is 7.

☛ Also Check:

GCF of 7 and 56 Examples

Example 1: For two numbers, GCF = 7 and LCM = 56. If one number is 7, find the other number.

Solution:

Given: GCF (x, 7) = 7 and LCM (x, 7) = 56
∵ GCF × LCM = 7 × (x)
⇒ x = (GCF × LCM)/7
⇒ x = (7 × 56)/7
⇒ x = 56
Therefore, the other number is 56.
Example 2: Find the greatest number that divides 7 and 56 exactly.

Solution:

The greatest number that divides 7 and 56 exactly is their greatest common factor, i.e. GCF of 7 and 56.
⇒ Factors of 7 and 56:
- Factors of 7 = 1, 7
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Therefore, the GCF of 7 and 56 is 7.
Example 3: The product of two numbers is 392. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of numbers = 392
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 392/7
Therefore, the LCM is 56.

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FAQs on GCF of 7 and 56

What is the GCF of 7 and 56?

The GCF of 7 and 56 is 7. To calculate the greatest common factor (GCF) of 7 and 56, we need to factor each number (factors of 7 = 1, 7; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56) and choose the greatest factor that exactly divides both 7 and 56, i.e., 7.

What are the Methods to Find GCF of 7 and 56?

There are three commonly used methods to find the GCF of 7 and 56.

By Euclidean Algorithm
By Long Division
By Prime Factorization

What is the Relation Between LCM and GCF of 7, 56?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 7 and 56, i.e. GCF × LCM = 7 × 56.

How to Find the GCF of 7 and 56 by Prime Factorization?

To find the GCF of 7 and 56, we will find the prime factorization of the given numbers, i.e. 7 = 7; 56 = 2 × 2 × 2 × 7.
⇒ Since 7 is the only common prime factor of 7 and 56. Hence, GCF (7, 56) = 7.
☛ Prime Number

How to Find the GCF of 7 and 56 by Long Division Method?

To find the GCF of 7, 56 using long division method, 56 is divided by 7. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

If the GCF of 56 and 7 is 7, Find its LCM.

GCF(56, 7) × LCM(56, 7) = 56 × 7
Since the GCF of 56 and 7 = 7
⇒ 7 × LCM(56, 7) = 392
Therefore, LCM = 56
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