GCF the 45 and also 60 is the largest possible number that divides 45 and also 60 precisely without any type of remainder. The factors of 45 and also 60 space 1, 3, 5, 9, 15, 45 and also 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There are 3 generally used methods to find the GCF the 45 and 60 - Euclidean algorithm, long division, and prime factorization.

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1. | GCF the 45 and 60 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF the 45 and also 60 is 15.

**Explanation: **

The GCF of 2 non-zero integers, x(45) and y(60), is the best positive creature m(15) that divides both x(45) and y(60) without any remainder.

The methods to find the GCF the 45 and 60 are described below.

Long division MethodPrime administrate MethodListing usual Factors### GCF that 45 and 60 by long Division

GCF of 45 and also 60 is the divisor the we obtain when the remainder becomes 0 after ~ doing long division repeatedly.

**Step 2:**due to the fact that the remainder ≠ 0, we will certainly divide the divisor of action 1 (45) through the remainder (15).

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

The equivalent divisor (15) is the GCF of 45 and also 60.

### GCF the 45 and also 60 by element Factorization

Prime factorization of 45 and also 60 is (3 × 3 × 5) and (2 × 2 × 3 × 5) respectively. As visible, 45 and 60 have common prime factors. Hence, the GCF of 45 and 60 is 3 × 5 = 15.

### GCF that 45 and 60 through Listing usual Factors

**Factors of 45:**1, 3, 5, 9, 15, 45

**Factors that 60:**1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There space 4 typical factors the 45 and also 60, that space 1, 3, 5, and 15. Therefore, the greatest common factor the 45 and also 60 is 15.

**☛ additionally Check:**

## GCF the 45 and also 60 Examples

**Example 1: The product of 2 numbers is 2700. If your GCF is 15, what is your LCM? **

**Solution:**

Given: GCF = 15 and also product of number = 2700∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 2700/15Therefore, the LCM is 180.

**Example 2: For 2 numbers, GCF = 15 and also LCM = 180. If one number is 45, find the various other number.**

**Solution:**

Given: GCF (x, 45) = 15 and also LCM (x, 45) = 180∵ GCF × LCM = 45 × (x)⇒ x = (GCF × LCM)/45⇒ x = (15 × 180)/45⇒ x = 60Therefore, the various other number is 60.

**Example 3: find the greatest number the divides 45 and 60 exactly. **

**Solution: **

The biggest number the divides 45 and 60 precisely is your greatest typical factor, i.e. GCF that 45 and 60.⇒ factors of 45 and also 60:

Factors that 45 = 1, 3, 5, 9, 15, 45Factors the 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60Therefore, the GCF of 45 and also 60 is 15.

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## FAQs top top GCF of 45 and 60

### What is the GCF the 45 and also 60?

The **GCF the 45 and also 60 is 15**. To calculate the GCF (Greatest typical Factor) that 45 and also 60, we need to element each number (factors the 45 = 1, 3, 5, 9, 15, 45; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest variable that exactly divides both 45 and also 60, i.e., 15.

### How to uncover the GCF of 45 and also 60 by element Factorization?

To find the GCF that 45 and 60, us will find the element factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 60 = 2 × 2 × 3 × 5.⇒ due to the fact that 3, 5 are common terms in the element factorization that 45 and 60. Hence, GCF(45, 60) = 3 × 5 = 15☛ element Number

### What is the Relation between LCM and GCF that 45, 60?

The adhering to equation have the right to be offered to refer the relation between Least common Multiple and also GCF that 45 and 60, i.e. GCF × LCM = 45 × 60.

### If the GCF of 60 and also 45 is 15, uncover its LCM.

GCF(60, 45) × LCM(60, 45) = 60 × 45Since the GCF that 60 and also 45 = 15⇒ 15 × LCM(60, 45) = 2700Therefore, LCM = 180☛ Greatest usual Factor Calculator

### How to uncover the GCF the 45 and also 60 by Long department Method?

To uncover the GCF the 45, 60 using long division method, 60 is split by 45. The matching divisor (15) as soon as remainder amounts to 0 is taken together GCF.

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### What space the techniques to find GCF the 45 and 60?

There room three commonly used methods to uncover the **GCF of 45 and also 60**.