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

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1. | GCF of 8 and 14 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF of 8 and 14 is 2.

**Explanation: **

The GCF of two non-zero integers, x(8) and y(14), is the greatest positive integer m(2) that divides both x(8) and y(14) without any remainder.

The methods to find the GCF of 8 and 14 are explained below.

Prime Factorization MethodListing Common FactorsUsing Euclid's Algorithm### GCF of 8 and 14 by Prime Factorization

Prime factorization of 8 and 14 is (2 × 2 × 2) and (2 × 7) respectively. As visible, 8 and 14 have only one common prime factor i.e. 2. Hence, the GCF of 8 and 14 is 2.

### GCF of 8 and 14 by Listing Common Factors

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

**Factors of 14:**1, 2, 7, 14

There are 2 common factors of 8 and 14, that are 1 and 2. Therefore, the greatest common factor of 8 and 14 is 2.

### GCF of 8 and 14 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 = 14 and Y = 8

GCF(14, 8) = GCF(8, 14 mod 8) = GCF(8, 6)GCF(8, 6) = GCF(6, 8 mod 6) = GCF(6, 2)GCF(6, 2) = GCF(2, 6 mod 2) = GCF(2, 0)GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)Therefore, the value of GCF of 8 and 14 is 2.

**☛ Also Check:**

## GCF of 8 and 14 Examples

**Example 1: Find the GCF of 8 and 14, if their LCM is 56. **

**Solution: **

∵ LCM × GCF = 8 × 14⇒ GCF(8, 14) = (8 × 14)/56 = 2Therefore, the greatest common factor of 8 and 14 is 2.

**Example 2: The product of two numbers is 112. If their GCF is 2, what is their LCM? **

**Solution:**

Given: GCF = 2 and product of numbers = 112∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 112/2Therefore, the LCM is 56.

**Example 3: For two numbers, GCF = 2 and LCM = 56. If one number is 14, find the other number.**

**Solution:**

Given: GCF (z, 14) = 2 and LCM (z, 14) = 56∵ GCF × LCM = 14 × (z)⇒ z = (GCF × LCM)/14⇒ z = (2 × 56)/14⇒ z = 8Therefore, the other number is 8.

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## FAQs on GCF of 8 and 14

### What is the GCF of 8 and 14?

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

### What are the Methods to Find GCF of 8 and 14?

There are three commonly used methods to find the **GCF of 8 and 14**.

### How to Find the GCF of 8 and 14 by Prime Factorization?

To find the GCF of 8 and 14, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 14 = 2 × 7.⇒ Since 2 is the only common prime factor of 8 and 14. Hence, GCF (8, 14) = 2.☛ Prime Number

### If the GCF of 14 and 8 is 2, Find its LCM.

GCF(14, 8) × LCM(14, 8) = 14 × 8Since the GCF of 14 and 8 = 2⇒ 2 × LCM(14, 8) = 112Therefore, LCM = 56☛ Greatest Common Factor Calculator

### How to Find the GCF of 8 and 14 by Long Division Method?

To find the GCF of 8, 14 using long division method, 14 is divided by 8. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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### What is the Relation Between LCM and GCF of 8, 14?

The following equation can be used to express the relation between Least Common Multiple and GCF of 8 and 14, i.e. GCF × LCM = 8 × 14.