GCF that 15 and also 25 is the largest feasible number that divides 15 and also 25 specifically without any type of remainder. The components of 15 and 25 are 1, 3, 5, 15 and also 1, 5, 25 respectively. There space 3 frequently used approaches to uncover the GCF of 15 and 25 - element factorization, lengthy division, and also Euclidean algorithm.

You are watching: What is the gcf of 15 and 25

1. | GCF the 15 and also 25 |

2. | List the Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF of 15 and 25 is 5.

**Explanation: **

The GCF of two non-zero integers, x(15) and also y(25), is the biggest positive essence m(5) the divides both x(15) and also y(25) without any type of remainder.

The techniques to find the GCF of 15 and also 25 are explained below.

Using Euclid's AlgorithmListing common FactorsPrime factorization Method### GCF the 15 and also 25 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)where X > Y and also mod is the modulo operator.

Here X = 25 and also Y = 15

GCF(25, 15) = GCF(15, 25 mode 15) = GCF(15, 10)GCF(15, 10) = GCF(10, 15 mod 10) = GCF(10, 5)GCF(10, 5) = GCF(5, 10 mode 5) = GCF(5, 0)GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)Therefore, the worth of GCF of 15 and 25 is 5.

### GCF of 15 and 25 by Listing typical Factors

**Factors the 15:**1, 3, 5, 15

**Factors that 25:**1, 5, 25

There space 2 common factors of 15 and 25, that are 1 and also 5. Therefore, the greatest common factor of 15 and also 25 is 5.

### GCF of 15 and also 25 by prime Factorization

Prime factorization of 15 and also 25 is (3 × 5) and (5 × 5) respectively. Together visible, 15 and 25 have only one common prime element i.e. 5. Hence, the GCF of 15 and 25 is 5.

**☛ additionally Check:**

## GCF the 15 and also 25 Examples

**Example 1: The product of 2 numbers is 375. If their GCF is 5, what is their LCM? **

**Solution:**

Given: GCF = 5 and also product of number = 375∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 375/5Therefore, the LCM is 75.

**Example 2: For two numbers, GCF = 5 and LCM = 75. If one number is 15, find the various other number.**

**Solution:**

Given: GCF (y, 15) = 5 and LCM (y, 15) = 75∵ GCF × LCM = 15 × (y)⇒ y = (GCF × LCM)/15⇒ y = (5 × 75)/15⇒ y = 25Therefore, the other number is 25.

**Example 3: find the GCF of 15 and also 25, if your LCM is 75. **

**Solution: **

∵ LCM × GCF = 15 × 25⇒ GCF(15, 25) = (15 × 25)/75 = 5Therefore, the greatest common factor that 15 and also 25 is 5.

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## FAQs ~ above GCF of 15 and 25

### What is the GCF of 15 and also 25?

The **GCF the 15 and also 25 is 5**. To calculate the greatest usual factor the 15 and 25, we need to element each number (factors of 15 = 1, 3, 5, 15; determinants of 25 = 1, 5, 25) and choose the greatest element that exactly divides both 15 and also 25, i.e., 5.

### What is the Relation between LCM and also GCF of 15, 25?

The complying with equation deserve to be used to express the relation in between Least common Multiple and also GCF that 15 and 25, i.e. GCF × LCM = 15 × 25.

### What room the techniques to uncover GCF that 15 and also 25?

There room three commonly used techniques to uncover the **GCF the 15 and 25**.

### How to discover the GCF the 15 and 25 by Long department Method?

To uncover the GCF the 15, 25 using long department method, 25 is separated by 15. The equivalent divisor (5) when remainder equals 0 is taken together GCF.

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### How to find the GCF the 15 and 25 by element Factorization?

To discover the GCF the 15 and 25, we will discover the prime factorization that the given numbers, i.e. 15 = 3 × 5; 25 = 5 × 5.⇒ because 5 is the only common prime factor of 15 and also 25. Hence, GCF (15, 25) = 5.☛ element Numbers

### If the GCF of 25 and 15 is 5, uncover its LCM.

GCF(25, 15) × LCM(25, 15) = 25 × 15Since the GCF the 25 and 15 = 5⇒ 5 × LCM(25, 15) = 375Therefore, LCM = 75☛ Greatest usual Factor Calculator