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GCF of 77 and 56

GCF of 77 and 56 is the largest possible number that divides 77 and 56 exactly without any remainder. The factors of 77 and 56 are 1, 7, 11, 77 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 commonly used methods to find the GCF of 77 and 56 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 77 and 56
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 77 and 56?

Answer: GCF of 77 and 56 is 7.

Explanation:

The GCF of two non-zero integers, x(77) and y(56), is the greatest positive integer m(7) that divides both x(77) and y(56) without any remainder.

Methods to Find GCF of 77 and 56

The methods to find the GCF of 77 and 56 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 77 and 56 by Listing Common Factors

Factors of 77: 1, 7, 11, 77
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56

There are 2 common factors of 77 and 56, that are 1 and 7. Therefore, the greatest common factor of 77 and 56 is 7.

GCF of 77 and 56 by Long Division

GCF of 77 and 56 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 77 (larger number) by 56 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (56) by the remainder (21).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the GCF of 77 and 56.

GCF of 77 and 56 by Prime Factorization

Prime factorization of 77 and 56 is (7 × 11) and (2 × 2 × 2 × 7) respectively. As visible, 77 and 56 have only one common prime factor i.e. 7. Hence, the GCF of 77 and 56 is 7.

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GCF of 77 and 56 Examples

Example 1: For two numbers, GCF = 7 and LCM = 616. If one number is 56, find the other number.

Solution:

Given: GCF (z, 56) = 7 and LCM (z, 56) = 616
∵ GCF × LCM = 56 × (z)
⇒ z = (GCF × LCM)/56
⇒ z = (7 × 616)/56
⇒ z = 77
Therefore, the other number is 77.
Example 2: Find the GCF of 77 and 56, if their LCM is 616.

Solution:

∵ LCM × GCF = 77 × 56
⇒ GCF(77, 56) = (77 × 56)/616 = 7
Therefore, the greatest common factor of 77 and 56 is 7.
Example 3: Find the greatest number that divides 77 and 56 exactly.

Solution:

The greatest number that divides 77 and 56 exactly is their greatest common factor, i.e. GCF of 77 and 56.
⇒ Factors of 77 and 56:
- Factors of 77 = 1, 7, 11, 77
- Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Therefore, the GCF of 77 and 56 is 7.

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FAQs on GCF of 77 and 56

What is the GCF of 77 and 56?

The GCF of 77 and 56 is 7. To calculate the GCF of 77 and 56, we need to factor each number (factors of 77 = 1, 7, 11, 77; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56) and choose the greatest factor that exactly divides both 77 and 56, i.e., 7.

How to Find the GCF of 77 and 56 by Long Division Method?

To find the GCF of 77, 56 using long division method, 77 is divided by 56. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 77, 56?

The following equation can be used to express the relation between LCM and GCF of 77 and 56, i.e. GCF × LCM = 77 × 56.

If the GCF of 56 and 77 is 7, Find its LCM.

GCF(56, 77) × LCM(56, 77) = 56 × 77
Since the GCF of 56 and 77 = 7
⇒ 7 × LCM(56, 77) = 4312
Therefore, LCM = 616
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What are the Methods to Find GCF of 77 and 56?

There are three commonly used methods to find the GCF of 77 and 56.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 77 and 56 by Prime Factorization?

To find the GCF of 77 and 56, we will find the prime factorization of the given numbers, i.e. 77 = 7 × 11; 56 = 2 × 2 × 2 × 7.
⇒ Since 7 is the only common prime factor of 77 and 56. Hence, GCF (77, 56) = 7.
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