Greatest Common Factor (GCF)

Find the highest common factor of the given numbers

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Greatest Common Factor

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Number 1

Number 2

Number 3

Find GCF

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

gcf-division-method

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.

gcf-prime-factorization-method

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

GCF Input	GCF / GCD / HCF Output
gcf of 12 and 18	6
gcf of 8 and 12	4
gcf of 16 and 24	8
gcf of 24 and 36	12
gcf of 18 and 24	6
gcf of 12 and 16	4
gcf of 12 and 20	4
gcf of 24 and 40	8
gcf of 24 and 32	8
gcf of 36 and 48	12
gcf of 32 and 48	16
gcf of 27 and 36	9
gcf of 30 and 45	15
gcf of 6 and 8	2
gcf of 12 and 30	6
gcf of 16 and 28	4
gcf of 18 and 27	9
gcf of 36 and 54	18
gcf of 28 and 42	14
gcf of 15 and 20	5
gcf of 16 and 20	4
gcf of 24 and 30	6
gcf of 6 and 9	3
gcf of 6 and 15	3
gcf of 4 and 12	4
gcf of 36 and 60	12
gcf of 15 and 10	5
gcf of 9 and 15	3
gcf of 45 and 60	15
gcf of 8 and 10	2
gcf of 24 and 60	12
gcf of 9 and 18	9
gcf of 30 and 15	15
gcf of 12 and 15	3
gcf of 6 and 12	6
gcf of 48 and 72	24
gcf of 14 and 28	14
gcf of 8 and 16	8
gcf of 6 and 18	6
gcf of 27 and 45	9
gcf of 18 and 42	6
gcf of 4 and 10	2
gcf of 6 and 10	2
gcf of 48 and 18	6
gcf of 20 and 24	4
gcf of 15 and 45	15
gcf of 30 and 42	6
gcf of 32 and 40	8
gcf of 24 and 72	24
gcf of 8 and 24	8
gcf of 36 and 42	6
gcf of 4 and 6	2
gcf of 5 and 10	5
gcf of 12 and 28	4
gcf of 10 and 25	5
gcf of 60 and 72	12
gcf of 24 and 42	6
gcf of 30 and 75	15
gcf of 42 and 56	14
gcf of 12 and 30	6
gcf of 72 and 90	18
gcf of 16 and 48	16
gcf of 14 and 42	14
gcf of 24 and 28	4
gcf of 9 and 36	9
gcf of 6 and 24	6
gcf of 20 and 32	4
gcf of 48 and 30	6
gcf of 32 and 8	8
gcf of 54 and 72	18
gcf of 24 and 48	24
gcf of 10 and 20	10
gcf of 3 and 6	3
gcf of 45 and 81	9
gcf of 7 and 14	7
gcf of 24 and 54	6
gcf of 16 and 18	2
gcf of 2 and 8	2
gcf of 15 and 24	3
gcf of 10 and 45	5
gcf of 32 and 80	16
gcf of 8 and 15	1
gcf of 12 and 21	3
gcf of 8 and 20	4
gcf of 20 and 16	4
gcf of 45 and 30	15
gcf of 40 and 60	20
gcf of 48 and 56	8
gcf of 3 and 12	3
gcf of 20 and 40	20
gcf of 30 and 50	10
gcf of 7 and 21	7
gcf of 20 and 30	10
gcf of 36 and 63	9
gcf of 18 and 21	3
gcf of 3 and 8	1
gcf of 28 and 12	4
gcf of 12 and 42	6
gcf of 40 and 64	8
gcf of 60 and 90	30
gcf of 10 and 35	5
gcf of 42 and 70	14
gcf of 5 and 6	1
gcf of 18 and 72	18
gcf of 15 and 12	3
gcf of 16 and 64	16
gcf of 3 and 18	3
gcf of 6 and 16	2
gcf of 63 and 84	21
gcf of 49 and 98	49
gcf of 36 and 90	18
gcf of 13 and 26	13
gcf of 25 and 75	25
gcf of 9 and 21	3
gcf of 14 and 16	2
gcf of 4 and 16	4
gcf of 10 and 14	2
gcf of 5 and 7	1
gcf of 25 and 45	5
gcf of 75 and 90	15
gcf of 4 and 8	4
gcf of 18 and 32	2
gcf of 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 mehtods to find HCF/GCF. By listing factors method, first List all the factors of each number separately and collect the common factors. Product of these common factors will be the HCF.