GCF of 27 and 63 is the largest possible number that divides 27 and 63 exactly without any remainder. The factors of 27 and 63 are 1, 3, 9, 27 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 27 and 63 – Euclidean algorithm, long division, and prime factorization.

You are watching: Greatest common factor of 27 and 63

1. | GCF of 27 and 63 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF of 27 and 63 is 9.

**Explanation: **

The GCF of two non-zero integers, x(27) and y(63), is the greatest positive integer m(9) that divides both x(27) and y(63) without any remainder.

Let's look at the different methods for finding the GCF of 27 and 63.

Prime Factorization MethodListing Common FactorsLong Division Method

### GCF of 27 and 63 by Prime Factorization

Prime factorization of 27 and 63 is (3 × 3 × 3) and (3 × 3 × 7) respectively. As visible, 27 and 63 have common prime factors. Hence, the GCF of 27 and 63 is 3 × 3 = 9.

### GCF of 27 and 63 by Listing Common Factors

**Factors of 27:** 1, 3, 9, 27**Factors of 63:** 1, 3, 7, 9, 21, 63

There are 3 common factors of 27 and 63, that are 1, 3, and 9. Therefore, the greatest common factor of 27 and 63 is 9.

### GCF of 27 and 63 by Long Division

GCF of 27 and 63 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 (27) by the remainder (9).

See more: What Is The Full Form Of Google ? What Does Google Mean

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

The corresponding divisor (9) is the GCF of 27 and 63.

**☛ Also Check:**

## GCF of 27 and 63 Examples

**Example 1: Find the greatest number that divides 27 and 63 exactly. **

**Solution: **

The greatest number that divides 27 and 63 exactly is their greatest common factor, i.e. GCF of 27 and 63.⇒ Factors of 27 and 63:

Factors of 27 = 1, 3, 9, 27Factors of 63 = 1, 3, 7, 9, 21, 63

Therefore, the GCF of 27 and 63 is 9.

**Example 2: The product of two numbers is 1701. If their GCF is 9, what is their LCM? **

**Solution:**

Given: GCF = 9 and product of numbers = 1701∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 1701/9Therefore, the LCM is 189.

**Example 3: For two numbers, GCF = 9 and LCM = 189. If one number is 27, find the other number.**

**Solution:**

Given: GCF (y, 27) = 9 and LCM (y, 27) = 189∵ GCF × LCM = 27 × (y)⇒ y = (GCF × LCM)/27⇒ y = (9 × 189)/27⇒ y = 63Therefore, the other number is 63.

Show Solution >

go to slidego to slidego to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

## FAQs on GCF of 27 and 63

### What is the GCF of 27 and 63?

The **GCF of 27 and 63 is 9**. To calculate the greatest common factor (GCF) of 27 and 63, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 27 and 63, i.e., 9.

### How to Find the GCF of 27 and 63 by Long Division Method?

To find the GCF of 27, 63 using long division method, 63 is divided by 27. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

### How to Find the GCF of 27 and 63 by Prime Factorization?

To find the GCF of 27 and 63, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 63 = 3 × 3 × 7.⇒ Since 3, 3 are common terms in the prime factorization of 27 and 63. Hence, GCF(27, 63) = 3 × 3 = 9☛ What is a Prime Number?

### If the GCF of 63 and 27 is 9, Find its LCM.

GCF(63, 27) × LCM(63, 27) = 63 × 27Since the GCF of 63 and 27 = 9⇒ 9 × LCM(63, 27) = 1701Therefore, LCM = 189☛ GCF Calculator

### What is the Relation Between LCM and GCF of 27, 63?

The following equation can be used to express the relation between LCM and GCF of 27 and 63, i.e. GCF × LCM = 27 × 63.

See more: What Type Of Gelatin Is In Pop Tarts Halal Or Haram? Pop Tarts Are Not Haram :): Islam

### What are the Methods to Find GCF of 27 and 63?

There are three commonly used methods to find the **GCF of 27 and 63**.