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Greatest Common Factor: 6

## What is GCF?

### Greatest Common Factor

Greatest Common Factor of any group of numbers is defined as the largest number that will be the factor of all the numbers in a group. Also called as Greatest Common Divisor or Highest Common Factor

A factor is the number which divides another number without leaving a remainder. for eg: 2 , 3 , 4 , 6 are the factors of 12.

## What Methods are there to find GCF (GCD/HCF)??

- Division Method
- Prime Factorization Method
- Grid Method
- Cake Method (Ladder Method)
- Box Method
- Listing factors Method

### Division Method to find GCF

- Step 1: Divide the greatest number by the smallest number from the given set of numbers
- Step 2: Now the remainder of above will be treated as divisor and divisor will be treated as dividend.
- Step 3: Divide the first divisor by first remainder.
- Step 4: Divide the second divisor(i.e first remainder) by second remainder.
- Step 5: Proceed with these steps untill you get remainder 0.
- Step 6: The last Divisor which leaves remainder as 0 is the GCF or HCF of the given numbers.

### Example: Steps to find GCF of 12 and 30 using Division method.

- Step 1: Divide 30 by 12.This leads to the remainder 6.
- Step 2: Now divide 12 by 6.This gives remainder 0.
- step 3: So the GCF is 6.
- Division Flow

### Prime Factorization method

- Step 1: Write down the prime factorization of each number
- Step 2: Now take all the common factors of the numbers.
- Step 3: Multiplication of the common factors will be the gcf of the numbers.
- Example: GCF of 12 and 24 using Prime factorization method.
Prime factorization of 12 = 2 x 2 x 3,

Prime factorization of 24 = 2 x 2 x 2 x 3

we have 2 , 2 and 3 as common factor take these factors. Leave other factors since they are not Common

Multiply 2 x 2 x 3 this will be the gcf of 12 and 24.

### Grid Method

- Step 1: Write down the number seperated by vertical line and horizontal line to seperate each grid.
- Step 2: Divide the numbers by prime number(should exactly divide all the numbers) and write the result in the next row grid.
- Step 3: Continue dividing the numbers till the last common factor.Product of the prime numbers in the left side grid will be the gcf of the numbers.

### Cake / Ladder Method

- Step 1: This method is the one of the easiest way to find the gcf of the numbers. Write down the number in the first layer.(layer looks like top of the cake |__|.)
- Step 2: Divide the Layer numbers by prime numbers which divides the numbers and leave 0 as the remainder .Write the result in the next Layer.
- Step 3: Continue dividing the cake layers till the last common factor.GCF is the product of the prime numbers in the left side of the layers.
- Example: GCF of 15 and 27

### Box Method

- Step 1: Write down the number seperated by vertical line and horizontal line.
- Step 2: Divide the numbers by common factors and write the result in the next line.
- Step 3: Continue dividing the numbers by till the last common factors.Product of the common factors will be the GCF of the numbers.

### Listing factors Method

- Step 1: List all the factors of each numbers seperately.
- Step 2: Collect the common factors of all numbers.
- Step 3: Product of all common factors will be the greatest common factor(GCF).This is also known as Greatest Common divisor or Highest Common Factor.

## Table of GCF / HCF of Most Common Numbers

Input | GCF / HCF Output |
---|---|

12 and 18 | 6 |

8 and 12 | 4 |

16 and 24 | 8 |

24 and 36 | 12 |

18 and 24 | 6 |

12 and 16 | 4 |

12 and 20 | 4 |

24 and 40 | 8 |

24 and 32 | 8 |

36 and 48 | 12 |

32 and 48 | 16 |

27 and 36 | 9 |

30 and 45 | 15 |

6 and 8 | 2 |

12 and 30 | 6 |

16 and 28 | 4 |

18 and 27 | 9 |

36 and 54 | 18 |

28 and 42 | 14 |

15 and 20 | 5 |

16 and 20 | 4 |

24 and 30 | 6 |

6 and 9 | 3 |

6 and 15 | 3 |

4 and 12 | 4 |

36 and 60 | 12 |

15 and 10 | 5 |

9 and 15 | 3 |

45 and 60 | 15 |

8 and 10 | 2 |

24 and 60 | 12 |

9 and 18 | 9 |

30 and 15 | 15 |

12 and 15 | 3 |

6 and 12 | 6 |

48 and 72 | 24 |

14 and 28 | 14 |

8 and 16 | 8 |

6 and 18 | 6 |

27 and 45 | 9 |

18 and 42 | 6 |

4 and 10 | 2 |

6 and 10 | 2 |

48 and 18 | 6 |

20 and 24 | 4 |

15 and 45 | 15 |

30 and 42 | 6 |

32 and 40 | 8 |

24 and 72 | 24 |

8 and 24 | 8 |

36 and 42 | 6 |

4 and 6 | 2 |

5 and 10 | 5 |

12 and 28 | 4 |

10 and 25 | 5 |

60 and 72 | 12 |

24 and 42 | 6 |

30 and 75 | 15 |

42 and 56 | 14 |

12 and 30 | 6 |

72 and 90 | 18 |

16 and 48 | 16 |

14 and 42 | 14 |

24 and 28 | 4 |

9 and 36 | 9 |

6 and 24 | 6 |

20 and 32 | 4 |

48 and 30 | 6 |

32 and 8 | 8 |

54 and 72 | 18 |

24 and 48 | 24 |

10 and 20 | 10 |

3 and 6 | 3 |

45 and 81 | 9 |

7 and 14 | 7 |

24 and 54 | 6 |

16 and 18 | 2 |

2 and 8 | 2 |

15 and 24 | 3 |

10 and 45 | 5 |

32 and 80 | 16 |

8 and 15 | 1 |

12 and 21 | 3 |

8 and 20 | 4 |

20 and 16 | 4 |

45 and 30 | 15 |

40 and 60 | 20 |

48 and 56 | 8 |

3 and 12 | 3 |

20 and 40 | 20 |

30 and 50 | 10 |

7 and 21 | 7 |

20 and 30 | 10 |

36 and 63 | 9 |

18 and 21 | 3 |

3 and 8 | 1 |

28 and 12 | 4 |

12 and 42 | 6 |

40 and 64 | 8 |

60 and 90 | 30 |

10 and 35 | 5 |

42 and 70 | 14 |

5 and 6 | 1 |

18 and 72 | 18 |

15 and 12 | 3 |

16 and 64 | 16 |

3 and 18 | 3 |

6 and 16 | 2 |

63 and 84 | 21 |

49 and 98 | 49 |

36 and 90 | 18 |

13 and 26 | 13 |

25 and 75 | 25 |

9 and 21 | 3 |

14 and 16 | 2 |

4 and 16 | 4 |

10 and 14 | 2 |

5 and 7 | 1 |

25 and 45 | 5 |

75 and 90 | 15 |

4 and 8 | 4 |

18 and 32 | 2 |

6 and 30 | 6 |

## Frequently Asked Questions on GCF

Greatest common factor of any group of numbers is defined as the largest number that will be the factor of all the numbers in a group.

There are various methods to find HCF/GCF. To find GCF by listing factors method, first identify all the factors of each number separately and collect the common factors.

Product of these common factors will be the HCF.

GCF facttoring is just taking out the common polynomial from the higher degree polynomials, which will make the problem to get solved easily.

GCF - G for Greatest , C for Common and F for Factor. HCF - H for Highest, C for Common and F for Factor