Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 21, 35 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 21 and 35 is **7**.

GCF(21,35) = 7

*Greatest common factor* or Greatest common divisor (GCD) can be calculated in following way;

- Greatest Common Factor of 21 and 35 by prime factorization method
- Greatest Common Factor of 21 and 35 by matching factors method

**Prime Factorization of 21**

3 | 21 |

7 | 7 |

1 |

Prime factors of 21 are 3,7. Prime factorization of **21** in exponential form is:

21 = 3^{1}×7^{1}

**Prime Factorization of 35**

5 | 35 |

7 | 7 |

1 |

Prime factors of 35 are 5,7. Prime factorization of **35** in exponential form is:

35 = 5^{1}×7^{1}

∴ So by taking common prime factors GCF of 21 and 35 is 7

**Factors of 21**

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

**Factors of 35**

List of positive integer factors of 35 that divides 35 without a remainder.

1,5,7,35

**Greatest Common Factor**

We found the factors and prime factorization of 21 and 35. The biggest common factor number is the **GCF** number.

So the **greatest common factor 21 and 35** is **7**.

Also check out the Least Common Multiple of 21 and 35

(i) The GCF of 21 and 35 is associative

GCF of 21 and 35 = GCF of 35 and 21

1. What is the GCF of 21 and 35?

Answer: GCF of 21 and 35 is 7.

2. What are the Factors of 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

3. What are the Factors of 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

4. How to Find the GCF of 21 and 35?

Answer:

Greatest Common Factor of 21 and 35 = 7

Step 1: Find the prime factorization of 21

21 = 3 x 7

Step 2: Find the prime factorization of 35

35 = 5 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 7

Step 4: Therefore, the greatest common factor of 21 and 35 is 7