GCF that 4 and also 10 is the largest feasible number that divides 4 and also 10 specifically without any remainder. The factors of 4 and 10 are 1, 2, 4 and also 1, 2, 5, 10 respectively. There are 3 generally used approaches to uncover the GCF that 4 and also 10 - element factorization, lengthy division, and Euclidean algorithm.

You are watching: What is the gcf of 4 and 10

1. | GCF that 4 and 10 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF of 4 and also 10 is 2.

**Explanation: **

The GCF of 2 non-zero integers, x(4) and y(10), is the biggest positive integer m(2) the divides both x(4) and also y(10) without any remainder.

Let's look at the different methods for finding the GCF of 4 and 10.

Listing usual FactorsLong division MethodPrime administer Method### GCF of 4 and 10 through Listing common Factors

**Factors that 4:**1, 2, 4

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

There space 2 usual factors that 4 and 10, that are 1 and also 2. Therefore, the greatest usual factor the 4 and also 10 is 2.

### GCF that 4 and also 10 by long Division

GCF that 4 and 10 is the divisor that we get when the remainder becomes 0 after doing long department repeatedly.

**Step 2:**because the remainder ≠ 0, we will divide the divisor of action 1 (4) by the remainder (2).

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

The corresponding divisor (2) is the GCF of 4 and 10.

### GCF the 4 and also 10 by prime Factorization

Prime administrate of 4 and also 10 is (2 × 2) and also (2 × 5) respectively. Together visible, 4 and 10 have actually only one usual prime variable i.e. 2. Hence, the GCF the 4 and also 10 is 2.

**☛ also Check:**

## GCF that 4 and 10 Examples

**Example 1: uncover the GCF of 4 and also 10, if their LCM is 20. **

**Solution: **

∵ LCM × GCF = 4 × 10⇒ GCF(4, 10) = (4 × 10)/20 = 2Therefore, the greatest usual factor the 4 and also 10 is 2.

**Example 2: The product of two numbers is 40. If their GCF is 2, what is their LCM? **

**Solution:**

Given: GCF = 2 and product of number = 40∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 40/2Therefore, the LCM is 20.

**Example 3: find the best number the divides 4 and 10 exactly. **

**Solution: **

The biggest number the divides 4 and 10 specifically is your greatest common factor, i.e. GCF the 4 and also 10.⇒ factors of 4 and 10:

Factors that 4 = 1, 2, 4Factors the 10 = 1, 2, 5, 10Therefore, the GCF that 4 and also 10 is 2.

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## FAQs on GCF of 4 and 10

### What is the GCF of 4 and 10?

The **GCF that 4 and also 10 is 2**. To calculate the greatest typical factor (GCF) of 4 and 10, we require to aspect each number (factors the 4 = 1, 2, 4; components of 10 = 1, 2, 5, 10) and choose the greatest variable that exactly divides both 4 and also 10, i.e., 2.

### How to find the GCF the 4 and also 10 by prime Factorization?

To uncover the GCF of 4 and also 10, we will uncover the prime factorization of the given numbers, i.e. 4 = 2 × 2; 10 = 2 × 5.⇒ because 2 is the only usual prime aspect of 4 and 10. Hence, GCF (4, 10) = 2.☛ prime Numbers

### If the GCF that 10 and also 4 is 2, discover its LCM.

GCF(10, 4) × LCM(10, 4) = 10 × 4Since the GCF that 10 and 4 = 2⇒ 2 × LCM(10, 4) = 40Therefore, LCM = 20☛ Greatest typical Factor Calculator

### How to find the GCF that 4 and 10 by Long division Method?

To find the GCF of 4, 10 using long division method, 10 is separated by 4. The corresponding divisor (2) once remainder amounts to 0 is taken as GCF.

### What space the approaches to uncover GCF of 4 and 10?

There space three commonly used methods to uncover the **GCF that 4 and also 10**.

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### What is the Relation between LCM and also GCF of 4, 10?

The following equation can be used to to express the relation between LCM (Least typical Multiple) and also GCF that 4 and 10, i.e. GCF × LCM = 4 × 10.