GCF the 21 and 35 is the largest possible number the divides 21 and 35 precisely without any remainder. The factors of 21 and 35 space 1, 3, 7, 21 and 1, 5, 7, 35 respectively. There space 3 generally used approaches to discover the GCF the 21 and 35 - prime factorization, lengthy division, and also Euclidean algorithm.

You are watching: What is the greatest common factor of 21 and 35

1. | GCF that 21 and also 35 |

2. | List the Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** GCF of 21 and 35 is 7.

**Explanation: **

The GCF of two non-zero integers, x(21) and y(35), is the biggest positive essence m(7) that divides both x(21) and y(35) without any remainder.

Let's look at the various methods for finding the GCF of 21 and also 35.

Long division MethodPrime administrate MethodListing typical Factors### GCF the 21 and also 35 by lengthy Division

GCF that 21 and 35 is the divisor the we gain when the remainder i do not care 0 ~ doing long department repeatedly.

**Step 2:**since the remainder ≠ 0, we will certainly divide the divisor of action 1 (21) by the remainder (14).

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

The corresponding divisor (7) is the GCF the 21 and also 35.

### GCF the 21 and also 35 by element Factorization

Prime administer of 21 and 35 is (3 × 7) and (5 × 7) respectively. As visible, 21 and also 35 have only one typical prime variable i.e. 7. Hence, the GCF of 21 and also 35 is 7.

### GCF that 21 and also 35 by Listing usual Factors

**Factors of 21:**1, 3, 7, 21

**Factors the 35:**1, 5, 7, 35

There room 2 usual factors of 21 and also 35, that are 1 and 7. Therefore, the greatest typical factor of 21 and also 35 is 7.

**☛ also Check:**

## GCF of 21 and also 35 Examples

**Example 1: The product of 2 numbers is 735. If your GCF is 7, what is your LCM? **

**Solution:**

Given: GCF = 7 and product of number = 735∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 735/7Therefore, the LCM is 105.

**Example 2: For 2 numbers, GCF = 7 and LCM = 105. If one number is 21, find the other number.**

**Solution:**

Given: GCF (x, 21) = 7 and also LCM (x, 21) = 105∵ GCF × LCM = 21 × (x)⇒ x = (GCF × LCM)/21⇒ x = (7 × 105)/21⇒ x = 35Therefore, the other number is 35.

**Example 3: find the GCF that 21 and also 35, if your LCM is 105. **

**Solution: **

∵ LCM × GCF = 21 × 35⇒ GCF(21, 35) = (21 × 35)/105 = 7Therefore, the greatest usual factor of 21 and also 35 is 7.

Show equipment >

go come slidego to slidego come slide

Ready to watch the world through math’s eyes?

Math is in ~ the main point of everything we do. Enjoy solving real-world math problems in live classes and become an experienced at everything.

Book a free Trial Class

## FAQs top top GCF the 21 and also 35

### What is the GCF that 21 and 35?

The **GCF that 21 and also 35 is 7**. To calculate the greatest usual factor (GCF) the 21 and 35, we require to factor each number (factors of 21 = 1, 3, 7, 21; components of 35 = 1, 5, 7, 35) and also choose the greatest aspect that exactly divides both 21 and also 35, i.e., 7.

### What space the techniques to find GCF of 21 and also 35?

There are three commonly used methods to discover the **GCF of 21 and also 35**.

### How to uncover the GCF of 21 and 35 through Long division Method?

To uncover the GCF of 21, 35 using long division method, 35 is split by 21. The matching divisor (7) once remainder amounts to 0 is taken together GCF.

### What is the Relation between LCM and also GCF that 21, 35?

The following equation can be supplied to express the relation in between Least usual Multiple and also GCF that 21 and 35, i.e. GCF × LCM = 21 × 35.

See more: Area Of A Kite Formula To Find The Area Of A Kite Area Calculator

### If the GCF that 35 and also 21 is 7, find its LCM.

GCF(35, 21) × LCM(35, 21) = 35 × 21Since the GCF the 35 and 21 = 7⇒ 7 × LCM(35, 21) = 735Therefore, LCM = 105☛ GCF Calculator

### How to find the GCF the 21 and also 35 by prime Factorization?

To uncover the GCF of 21 and 35, we will uncover the prime factorization of the given numbers, i.e. 21 = 3 × 7; 35 = 5 × 7.⇒ due to the fact that 7 is the only usual prime factor of 21 and 35. Hence, GCF (21, 35) = 7.☛ What room Prime Numbers?