How to Find GCF of 1812/312, 2028/839?

GCF of 1812/312, 2028/839

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 1812/312, 2028/839 i.e 12/261768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1812/312, 2028/839.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 1812/312,2028/839?

Given fractions are 1812/312,2028/839

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 1812/312,2028/839, numerators are 1812,2028

Denominators are 312,839

The GCF of 1812,2028 is 12 .

LCM of 312,839 is 261768.

The greatest common factor of 1812/312,2028/839 = [GCF of 1812,2028]/[LCM of 312,839]= 12/261768

Therefore, the GCF of 1812/312,2028/839 is 12/261768.

Greatest Common Factor of 1812,2028

To find the highest common factor of 1812,2028, we have to find the factors of both numbers and list the highest common factor.

The factors of 1812 are 1, 2, 3, 4, 6, 12, 151, 302, 453, 604, 906, 1812

The factors of 2028 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156, 169, 338, 507, 676, 1014, 2028

The HCF of 1812,2028 is 12.

Lets's calculate GCF of 1812,2028

Greatest Common Factor (GCF) of 1812,2028 By Common Division

2	1812, 2028
2	906, 1014
3	453, 507
	151, 169

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 1812,2028 By Matching Biggest Common Factor Method

Now, list down the factors of 1812

1,2,3,4,6,12,151,302,453,604,906,1812

Now, list down the factors of 2028

1,2,3,4,6,12,13,26,39,52,78,156,169,338,507,676,1014,2028

Greatest Common Factor

We found the factors 1812,2028 . The biggest common factor number is the GCF number.
So the greatest common factor 1812,2028 is 12.

Lets's calculate LCM of 312,839

Lowest Common Multiple of 312,839 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 261768

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/261768

Therefore, the GCF of Fractions 1812/312,2028/839 is 12/261768

Least Common Multiple of 312,839 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 312,839 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(312,839) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(312,839) x common factors =1 x 1 = 1

LCM(312,839) = ( 312 × 839 ) / 1

LCM(312,839) = 261768 / 1

LCM(312,839) = 261768

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 1812/312, 2028/839

1. What is the HCF of 1812,2028?

The HCF of 1812,2028 is 12

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 1812/312, 2028/839?

Answer: GCF of Numerators as per given numbers 1812/312, 2028/839 is

GCF of Numerators i.e. for 1812,2028 is 12

LCM of denominators i.e. for 312,839 is 261768.

Thus, GCF of Fractions is 12/261768.Finally, GCF of Fractions for 1812/312, 2028/839 is 12/261768.