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

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1. | GCF of 7 and 8 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF of 7 and 8 is 1.

**Explanation: **

The GCF of two non-zero integers, x(7) and y(8), is the greatest positive integer m(1) that divides both x(7) and y(8) without any remainder.

The methods to find the GCF of 7 and 8 are explained below.

Long Division MethodUsing Euclid's AlgorithmListing Common Factors### GCF of 7 and 8 by Long Division

GCF of 7 and 8 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

**Step 2:**Since the remainder ≠ 0, we will divide the divisor of step 1 (7) by the remainder (1).

**Step 3:**Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 7 and 8.

### GCF of 7 and 8 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 = 8 and Y = 7

GCF(8, 7) = GCF(7, 8 mod 7) = GCF(7, 1)GCF(7, 1) = GCF(1, 7 mod 1) = GCF(1, 0)GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)Therefore, the value of GCF of 7 and 8 is 1.

### GCF of 7 and 8 by Listing Common Factors

**Factors of 7:**1, 7

**Factors of 8:**1, 2, 4, 8

Since, 1 is the only common factor between 7 and 8. The Greatest Common Factor of 7 and 8 is 1.

**☛ Also Check:**

## GCF of 7 and 8 Examples

**Example 1: Find the greatest number that divides 7 and 8 exactly. **

**Solution: **

The greatest number that divides 7 and 8 exactly is their greatest common factor, i.e. GCF of 7 and 8.⇒ Factors of 7 and 8:

Factors of 7 = 1, 7Factors of 8 = 1, 2, 4, 8Therefore, the GCF of 7 and 8 is 1.

**Example 2: Find the GCF of 7 and 8, if their LCM is 56. **

**Solution: **

∵ LCM × GCF = 7 × 8⇒ GCF(7, 8) = (7 × 8)/56 = 1Therefore, the greatest common factor of 7 and 8 is 1.

**Example 3: For two numbers, GCF = 1 and LCM = 56. If one number is 7, find the other number.**

**Solution:**

Given: GCF (z, 7) = 1 and LCM (z, 7) = 56∵ GCF × LCM = 7 × (z)⇒ z = (GCF × LCM)/7⇒ z = (1 × 56)/7⇒ z = 8Therefore, the other number is 8.

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## FAQs on GCF of 7 and 8

### What is the GCF of 7 and 8?

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

### How to Find the GCF of 7 and 8 by Long Division Method?

To find the GCF of 7, 8 using long division method, 8 is divided by 7. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

### What are the Methods to Find GCF of 7 and 8?

There are three commonly used methods to find the **GCF of 7 and 8**.

### What is the Relation Between LCM and GCF of 7, 8?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 7 and 8, i.e. GCF × LCM = 7 × 8.

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### How to Find the GCF of 7 and 8 by Prime Factorization?

To find the GCF of 7 and 8, we will find the prime factorization of the given numbers, i.e. 7 = 7; 8 = 2 × 2 × 2.⇒ There is no common prime factor for 7 and 8. Hence, GCF (7, 8) = 1.☛ Prime Number

### If the GCF of 8 and 7 is 1, Find its LCM.

GCF(8, 7) × LCM(8, 7) = 8 × 7Since the GCF of 8 and 7 = 1⇒ 1 × LCM(8, 7) = 56Therefore, LCM = 56☛ Greatest Common Factor Calculator