GCF the 10 and also 30 is the largest feasible number that divides 10 and 30 specifically without any type of remainder. The components of 10 and also 30 are 1, 2, 5, 10 and also 1, 2, 3, 5, 6, 10, 15, 30 respectively. There space 3 frequently used techniques to find the GCF of 10 and also 30 - long division, element factorization, and Euclidean algorithm.

You are watching: What is the greatest common factor of 30 and 10

1. | GCF the 10 and also 30 |

2. | List that Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF the 10 and 30 is 10.

**Explanation: **

The GCF of 2 non-zero integers, x(10) and y(30), is the biggest positive creature m(10) that divides both x(10) and also y(30) without any remainder.

The approaches to find the GCF the 10 and also 30 are described below.

Prime factorization MethodUsing Euclid's AlgorithmLong department Method### GCF that 10 and 30 by prime Factorization

Prime administer of 10 and also 30 is (2 × 5) and (2 × 3 × 5) respectively. As visible, 10 and also 30 have usual prime factors. Hence, the GCF the 10 and 30 is 2 × 5 = 10.

### GCF of 10 and also 30 through Euclidean Algorithm

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

Here X = 30 and also Y = 10

GCF(30, 10) = GCF(10, 30 mode 10) = GCF(10, 0)GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)Therefore, the worth of GCF the 10 and also 30 is 10.

### GCF the 10 and 30 by lengthy Division

GCF that 10 and also 30 is the divisor the we get when the remainder becomes 0 ~ doing long department repeatedly.

**Step 2:**since the remainder = 0, the divisor (10) is the GCF of 10 and also 30.

The corresponding divisor (10) is the GCF the 10 and 30.

**☛ likewise Check:**

## GCF the 10 and also 30 Examples

**Example 1: discover the GCF that 10 and also 30, if their LCM is 30. **

**Solution: **

∵ LCM × GCF = 10 × 30⇒ GCF(10, 30) = (10 × 30)/30 = 10Therefore, the greatest common factor of 10 and 30 is 10.

**Example 2: The product of 2 numbers is 300. If your GCF is 10, what is their LCM? **

**Solution:**

Given: GCF = 10 and also product of number = 300∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 300/10Therefore, the LCM is 30.

**Example 3: uncover the best number that divides 10 and also 30 exactly. **

**Solution: **

The biggest number the divides 10 and 30 specifically is their greatest common factor, i.e. GCF of 10 and 30.⇒ determinants of 10 and 30:

Factors of 10 = 1, 2, 5, 10Factors that 30 = 1, 2, 3, 5, 6, 10, 15, 30Therefore, the GCF of 10 and 30 is 10.

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## FAQs on GCF that 10 and also 30

### What is the GCF that 10 and 30?

The **GCF the 10 and 30 is 10**. To calculation the greatest typical factor (GCF) the 10 and also 30, we need to aspect each number (factors of 10 = 1, 2, 5, 10; components of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and also choose the greatest factor that precisely divides both 10 and 30, i.e., 10.

### How to uncover the GCF of 10 and 30 through Long division Method?

To uncover the GCF the 10, 30 making use of long division method, 30 is divided by 10. The matching divisor (10) once remainder equates to 0 is taken together GCF.

### If the GCF the 30 and 10 is 10, find its LCM.

GCF(30, 10) × LCM(30, 10) = 30 × 10Since the GCF the 30 and 10 = 10⇒ 10 × LCM(30, 10) = 300Therefore, LCM = 30☛ Greatest typical Factor Calculator

### What is the Relation in between LCM and also GCF that 10, 30?

The adhering to equation have the right to be used to to express the relation in between Least common Multiple (LCM) and also GCF the 10 and also 30, i.e. GCF × LCM = 10 × 30.

See more: How Many Times Does 7 Go Into 45 ? How Many Times Does 7 Go Into 45

### What are the techniques to discover GCF of 10 and 30?

There room three commonly used techniques to find the **GCF that 10 and 30**.

### How to find the GCF of 10 and also 30 by prime Factorization?

To uncover the GCF that 10 and also 30, we will uncover the prime factorization of the provided numbers, i.e. 10 = 2 × 5; 30 = 2 × 3 × 5.⇒ due to the fact that 2, 5 are common terms in the prime factorization of 10 and 30. Hence, GCF(10, 30) = 2 × 5 = 10☛ element Number