**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 20, 26 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 20 and 26 is **2**.

GCF(20,26) = 2

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

**Prime Factorization of 20**

2 | 20 |

2 | 10 |

5 | 5 |

1 |

Prime factors of 20 are 2,5. Prime factorization of **20** in exponential form is:

20 = 2^{2}×5^{1}

**Prime Factorization of 26**

2 | 26 |

13 | 13 |

1 |

Prime factors of 26 are 2,13. Prime factorization of **26** in exponential form is:

26 = 2^{1}×13^{1}

∴ So by taking common prime factors GCF of 20 and 26 is 2

**Factors of 20**

List of positive integer factors of 20 that divides 20 without a remainder.

1,2,4,5,10,20

**Factors of 26**

List of positive integer factors of 26 that divides 26 without a remainder.

1,2,13,26

**Greatest Common Factor**

We found the factors and prime factorization of 20 and 26. The biggest common factor number is the **GCF** number.

So the **greatest common factor 20 and 26** is **2**.

Also check out the Least Common Multiple of 20 and 26

(i) The GCF of 20 and 26 is associative

GCF of 20 and 26 = GCF of 26 and 20

1. What is the GCF of 20 and 26?

Answer: GCF of 20 and 26 is 2.

2. What are the Factors of 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

3. What are the Factors of 26?

Answer: Factors of 26 are 1, 2, 13, 26. There are 4 integers that are factors of 26. The greatest factor of 26 is 26.

4. How to Find the GCF of 20 and 26?

Answer:

Greatest Common Factor of 20 and 26 = 2

Step 1: Find the prime factorization of 20

20 = 2 x 2 x 5

Step 2: Find the prime factorization of 26

26 = 2 x 13

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

GCF = 2

Step 4: Therefore, the greatest common factor of 20 and 26 is 2