GCF that 10 and 45 is the largest feasible number that divides 10 and also 45 exactly without any remainder. The factors of 10 and 45 are 1, 2, 5, 10 and 1, 3, 5, 9, 15, 45 respectively. There room 3 frequently used techniques to uncover the GCF that 10 and also 45 - lengthy division, Euclidean algorithm, and prime factorization.

You are watching: What is the gcf of 10 and 45

1. | GCF that 10 and also 45 |

2. | List that Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF of 10 and also 45 is 5.

**Explanation: **

The GCF of two non-zero integers, x(10) and y(45), is the greatest positive essence m(5) that divides both x(10) and also y(45) without any remainder.

Let's look at the various methods because that finding the GCF of 10 and also 45.

Listing common FactorsPrime factorization MethodLong department Method### GCF that 10 and 45 by Listing common Factors

**Factors the 10:**1, 2, 5, 10

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

There room 2 typical factors that 10 and 45, that are 1 and also 5. Therefore, the greatest usual factor the 10 and 45 is 5.

### GCF that 10 and also 45 by prime Factorization

Prime administer of 10 and also 45 is (2 × 5) and also (3 × 3 × 5) respectively. As visible, 10 and also 45 have actually only one usual prime element i.e. 5. Hence, the GCF of 10 and 45 is 5.

### GCF that 10 and also 45 by long Division

GCF that 10 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

**Step 2:**because the remainder ≠ 0, we will certainly divide the divisor of action 1 (10) by the remainder (5).

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

The matching divisor (5) is the GCF of 10 and also 45.

**☛ additionally Check:**

## GCF of 10 and also 45 Examples

**Example 1: find the greatest number that divides 10 and 45 exactly. **

**Solution: **

The greatest number the divides 10 and 45 exactly is your greatest usual factor, i.e. GCF the 10 and 45.⇒ factors of 10 and 45:

Factors of 10 = 1, 2, 5, 10Factors of 45 = 1, 3, 5, 9, 15, 45Therefore, the GCF that 10 and 45 is 5.

**Example 2: The product of 2 numbers is 450. If their GCF is 5, what is their LCM? **

**Solution:**

Given: GCF = 5 and product of number = 450∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 450/5Therefore, the LCM is 90.

**Example 3: discover the GCF the 10 and also 45, if your LCM is 90. **

**Solution: **

∵ LCM × GCF = 10 × 45⇒ GCF(10, 45) = (10 × 45)/90 = 5Therefore, the greatest common factor the 10 and 45 is 5.

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## FAQs ~ above GCF that 10 and also 45

### What is the GCF of 10 and 45?

The **GCF of 10 and also 45 is 5**. To calculation the GCF (Greatest typical Factor) the 10 and 45, we require to element each number (factors of 10 = 1, 2, 5, 10; components of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that specifically divides both 10 and also 45, i.e., 5.

### If the GCF that 45 and also 10 is 5, discover its LCM.

GCF(45, 10) × LCM(45, 10) = 45 × 10Since the GCF of 45 and 10 = 5⇒ 5 × LCM(45, 10) = 450Therefore, LCM = 90☛ GCF Calculator

### What is the Relation between LCM and GCF the 10, 45?

The adhering to equation have the right to be supplied to express the relation in between Least common Multiple (LCM) and also GCF of 10 and 45, i.e. GCF × LCM = 10 × 45.

### How to find the GCF of 10 and 45 by prime Factorization?

To find the GCF of 10 and also 45, we will uncover the prime factorization the the given numbers, i.e. 10 = 2 × 5; 45 = 3 × 3 × 5.⇒ because 5 is the only typical prime variable of 10 and 45. Hence, GCF (10, 45) = 5.☛ What is a prime Number?

### What space the methods to uncover GCF that 10 and also 45?

There are three generally used techniques to discover the **GCF the 10 and also 45**.

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### How to discover the GCF the 10 and 45 by Long division Method?

To find the GCF of 10, 45 using long division method, 45 is split by 10. The matching divisor (5) when remainder equals 0 is taken as GCF.