# Greatest Common Factor (GCF)

## Find the highest common factor of the given numbers

Home Math

Greatest Common Factor

You can input in any of the fields and get equivalent values.
=
=

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
• 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.

• 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