GCF the 27 and 36 is the largest feasible number that divides 27 and also 36 precisely without any type of remainder. The factors of 27 and also 36 room 1, 3, 9, 27 and also 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There space 3 frequently used methods to uncover the GCF that 27 and 36 - long division, prime factorization, and Euclidean algorithm.

You are watching: Greatest common factor of 27 and 36

1. | GCF of 27 and 36 |

2. | List the Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF the 27 and 36 is 9.

**Explanation: **

The GCF of two non-zero integers, x(27) and also y(36), is the best positive essence m(9) that divides both x(27) and also y(36) without any type of remainder.

Let's look at the various methods because that finding the GCF the 27 and also 36.

Prime administer MethodUsing Euclid's AlgorithmListing usual Factors### GCF the 27 and 36 by element Factorization

Prime factorization of 27 and 36 is (3 × 3 × 3) and (2 × 2 × 3 × 3) respectively. As visible, 27 and 36 have typical prime factors. Hence, the GCF of 27 and also 36 is 3 × 3 = 9.

### GCF the 27 and 36 by Euclidean Algorithm

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

Here X = 36 and also Y = 27

GCF(36, 27) = GCF(27, 36 mod 27) = GCF(27, 9)GCF(27, 9) = GCF(9, 27 mode 9) = GCF(9, 0)GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, where X ≠ 0)Therefore, the worth of GCF that 27 and also 36 is 9.

### GCF of 27 and also 36 through Listing common Factors

**Factors that 27:**1, 3, 9, 27

**Factors of 36:**1, 2, 3, 4, 6, 9, 12, 18, 36

There space 3 typical factors that 27 and 36, that room 1, 3, and 9. Therefore, the greatest common factor of 27 and 36 is 9.

**☛ additionally Check:**

## GCF of 27 and also 36 Examples

**Example 1: discover the GCF that 27 and also 36, if their LCM is 108. **

**Solution: **

∵ LCM × GCF = 27 × 36⇒ GCF(27, 36) = (27 × 36)/108 = 9Therefore, the greatest usual factor the 27 and 36 is 9.

**Example 2: For 2 numbers, GCF = 9 and also LCM = 108. If one number is 36, find the other number.**

**Solution:**

Given: GCF (y, 36) = 9 and also LCM (y, 36) = 108∵ GCF × LCM = 36 × (y)⇒ y = (GCF × LCM)/36⇒ y = (9 × 108)/36⇒ y = 27Therefore, the other number is 27.

**Example 3: The product of 2 numbers is 972. If your GCF is 9, what is your LCM? **

**Solution:**

Given: GCF = 9 and product of number = 972∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 972/9Therefore, the LCM is 108.

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## FAQs ~ above GCF that 27 and also 36

### What is the GCF the 27 and also 36?

The **GCF the 27 and 36 is 9**. To calculate the greatest usual factor (GCF) of 27 and 36, we require to factor each number (factors the 27 = 1, 3, 9, 27; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and also choose the greatest factor that exactly divides both 27 and 36, i.e., 9.

### How to discover the GCF that 27 and also 36 by element Factorization?

To find the GCF of 27 and also 36, us will find the prime factorization the the provided numbers, i.e. 27 = 3 × 3 × 3; 36 = 2 × 2 × 3 × 3.⇒ since 3, 3 are typical terms in the element factorization that 27 and also 36. Hence, GCF(27, 36) = 3 × 3 = 9☛ What is a element Number?

### If the GCF of 36 and 27 is 9, discover its LCM.

GCF(36, 27) × LCM(36, 27) = 36 × 27Since the GCF of 36 and also 27 = 9⇒ 9 × LCM(36, 27) = 972Therefore, LCM = 108☛ GCF Calculator

### How to discover the GCF of 27 and 36 by Long department Method?

To find the GCF that 27, 36 utilizing long division method, 36 is divided by 27. The equivalent divisor (9) when remainder equates to 0 is taken together GCF.

### What room the methods to find GCF of 27 and also 36?

There space three commonly used approaches to find the **GCF that 27 and also 36**.

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### What is the Relation in between LCM and also GCF of 27, 36?

The complying with equation deserve to be used to to express the relation in between LCM (Least common Multiple) and GCF the 27 and 36, i.e. GCF × LCM = 27 × 36.