How to Find GCF of 804/123, 420/853?

GCF of 804/123, 420/853

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 804/123, 420/853 i.e 12/104919 easily. The following is the detailed procedure to determine the greatest common factor of fractions 804/123, 420/853.

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 804/123,420/853?

Given fractions are 804/123,420/853

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 804/123,420/853, numerators are 804,420

Denominators are 123,853

The GCF of 804,420 is 12 .

LCM of 123,853 is 104919.

The greatest common factor of 804/123,420/853 = [GCF of 804,420]/[LCM of 123,853]= 12/104919

Therefore, the GCF of 804/123,420/853 is 12/104919.

Greatest Common Factor of 804,420

To find the highest common factor of 804,420, we have to find the factors of both numbers and list the highest common factor.

The factors of 804 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

The HCF of 804,420 is 12.

Lets's calculate GCF of 804,420

Greatest Common Factor (GCF) of 804,420 By Common Division

2	804, 420
2	402, 210
3	201, 105
	67, 35

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

Greatest Common Factor of 804,420 By Matching Biggest Common Factor Method

Now, list down the factors of 804

1,2,3,4,6,12,67,134,201,268,402,804

Now, list down the factors of 420

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Greatest Common Factor

We found the factors 804,420 . The biggest common factor number is the GCF number.
So the greatest common factor 804,420 is 12.

Lets's calculate LCM of 123,853

Lowest Common Multiple of 123,853 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 104919

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/104919

Therefore, the GCF of Fractions 804/123,420/853 is 12/104919

Least Common Multiple of 123,853 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 123,853 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(123,853) = 1

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

GCF(123,853) x common factors =1 x 1 = 1

LCM(123,853) = ( 123 × 853 ) / 1

LCM(123,853) = 104919 / 1

LCM(123,853) = 104919

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FAQs on GCF of Fractions of 804/123, 420/853

1. What is the HCF of 804,420?

The HCF of 804,420 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 804/123, 420/853?

Answer: GCF of Numerators as per given numbers 804/123, 420/853 is

GCF of Numerators i.e. for 804,420 is 12

LCM of denominators i.e. for 123,853 is 104919.

Thus, GCF of Fractions is 12/104919.Finally, GCF of Fractions for 804/123, 420/853 is 12/104919.