How to Find GCF of 810/209, 6492/978?

GCF of 810/209, 6492/978

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 810/209, 6492/978 i.e 6/204402 easily. The following is the detailed procedure to determine the greatest common factor of fractions 810/209, 6492/978.

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 810/209,6492/978?

Given fractions are 810/209,6492/978

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 810/209,6492/978, numerators are 810,6492

Denominators are 209,978

The GCF of 810,6492 is 6 .

LCM of 209,978 is 204402.

The greatest common factor of 810/209,6492/978 = [GCF of 810,6492]/[LCM of 209,978]= 6/204402

Therefore, the GCF of 810/209,6492/978 is 6/204402.

Greatest Common Factor of 810,6492

To find the highest common factor of 810,6492, we have to find the factors of both numbers and list the highest common factor.

The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810

The factors of 6492 are 1, 2, 3, 4, 6, 12, 541, 1082, 1623, 2164, 3246, 6492

The HCF of 810,6492 is 6.

Lets's calculate GCF of 810,6492

Greatest Common Factor (GCF) of 810,6492 By Common Division

2	810, 6492
3	405, 3246
	135, 1082

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 810,6492 By Matching Biggest Common Factor Method

Now, list down the factors of 810

1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810

Now, list down the factors of 6492

1,2,3,4,6,12,541,1082,1623,2164,3246,6492

Greatest Common Factor

We found the factors 810,6492 . The biggest common factor number is the GCF number.
So the greatest common factor 810,6492 is 6.

Lets's calculate LCM of 209,978

Lowest Common Multiple of 209,978 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 204402

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/204402

Therefore, the GCF of Fractions 810/209,6492/978 is 6/204402

Least Common Multiple of 209,978 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 209,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(209,978) = 1

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

GCF(209,978) x common factors =1 x 1 = 1

LCM(209,978) = ( 209 × 978 ) / 1

LCM(209,978) = 204402 / 1

LCM(209,978) = 204402

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 810/209, 6492/978

1. What is the HCF of 810,6492?

The HCF of 810,6492 is 6

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 810/209, 6492/978?

Answer: GCF of Numerators as per given numbers 810/209, 6492/978 is

GCF of Numerators i.e. for 810,6492 is 6

LCM of denominators i.e. for 209,978 is 204402.

Thus, GCF of Fractions is 6/204402.Finally, GCF of Fractions for 810/209, 6492/978 is 6/204402.