GCF of 27 and 36 is the largest feasible number the divides 27 and 36 exactly without any kind of remainder. The determinants of 27 and 36 are 1, 3, 9, 27 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There room 3 typically used approaches to uncover the GCF of 27 and also 36 - long division, element factorization, and also Euclidean algorithm.

You are watching: What is the gcf of 27 and 36

1. | GCF the 27 and also 36 |

2. | List that Methods |

3. | Solved Examples |

4. | FAQs |

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

**Explanation: **

The GCF of 2 non-zero integers, x(27) and also y(36), is the best positive creature m(9) that divides both x(27) and y(36) without any remainder.

Let's look at the various methods for finding the GCF of 27 and also 36.

Prime administer MethodUsing Euclid's AlgorithmListing usual Factors### GCF of 27 and also 36 by prime Factorization

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

### GCF that 27 and also 36 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 = 36 and also Y = 27

GCF(36, 27) = GCF(27, 36 mod 27) = GCF(27, 9)GCF(27, 9) = GCF(9, 27 mod 9) = GCF(9, 0)GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)Therefore, the value of GCF the 27 and 36 is 9.

### GCF that 27 and 36 by Listing usual Factors

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

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

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

**☛ additionally Check:**

## GCF that 27 and also 36 Examples

**Example 1: discover the GCF of 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 two numbers, GCF = 9 and also LCM = 108. If one number is 36, discover the various other number.**

**Solution:**

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

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

**Solution:**

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

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## FAQs on GCF that 27 and also 36

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

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

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

To find the GCF that 27 and also 36, we will uncover the prime factorization the the given numbers, i.e. 27 = 3 × 3 × 3; 36 = 2 × 2 × 3 × 3.⇒ due to the fact that 3, 3 are typical terms in the prime factorization the 27 and also 36. Hence, GCF(27, 36) = 3 × 3 = 9☛ What is a prime Number?

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

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

### How to find the GCF that 27 and also 36 by Long department Method?

To discover the GCF that 27, 36 making use of long division method, 36 is divided by 27. The corresponding divisor (9) when remainder amounts to 0 is taken as GCF.

### What space the techniques to discover GCF that 27 and 36?

There are three commonly used methods to uncover the **GCF that 27 and also 36**.

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

The following equation have the right to be provided to refer the relation in between LCM (Least usual Multiple) and GCF that 27 and also 36, i.e. GCF × LCM = 27 × 36.