How to Find GCF of 8478/262, 8212/827?

GCF of 8478/262, 8212/827

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 8478/262, 8212/827 i.e 2/216674 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8478/262, 8212/827.

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 8478/262,8212/827?

Given fractions are 8478/262,8212/827

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 8478/262,8212/827, numerators are 8478,8212

Denominators are 262,827

The GCF of 8478,8212 is 2 .

LCM of 262,827 is 216674.

The greatest common factor of 8478/262,8212/827 = [GCF of 8478,8212]/[LCM of 262,827]= 2/216674

Therefore, the GCF of 8478/262,8212/827 is 2/216674.

Greatest Common Factor of 8478,8212

To find the highest common factor of 8478,8212, we have to find the factors of both numbers and list the highest common factor.

The factors of 8478 are 1, 2, 3, 6, 9, 18, 27, 54, 157, 314, 471, 942, 1413, 2826, 4239, 8478

The factors of 8212 are 1, 2, 4, 2053, 4106, 8212

The HCF of 8478,8212 is 2.

Lets's calculate GCF of 8478,8212

Greatest Common Factor (GCF) of 8478,8212 By Common Division

2	8478, 8212
	4239, 4106

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 8478,8212 By Matching Biggest Common Factor Method

Now, list down the factors of 8478

1,2,3,6,9,18,27,54,157,314,471,942,1413,2826,4239,8478

Now, list down the factors of 8212

1,2,4,2053,4106,8212

Greatest Common Factor

We found the factors 8478,8212 . The biggest common factor number is the GCF number.
So the greatest common factor 8478,8212 is 2.

Lets's calculate LCM of 262,827

Lowest Common Multiple of 262,827 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 216674

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/216674

Therefore, the GCF of Fractions 8478/262,8212/827 is 2/216674

Least Common Multiple of 262,827 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 262,827 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(262,827) = 1

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

GCF(262,827) x common factors =1 x 1 = 1

LCM(262,827) = ( 262 × 827 ) / 1

LCM(262,827) = 216674 / 1

LCM(262,827) = 216674

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FAQs on GCF of Fractions of 8478/262, 8212/827

1. What is the HCF of 8478,8212?

The HCF of 8478,8212 is 2

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 8478/262, 8212/827?

Answer: GCF of Numerators as per given numbers 8478/262, 8212/827 is

GCF of Numerators i.e. for 8478,8212 is 2

LCM of denominators i.e. for 262,827 is 216674.

Thus, GCF of Fractions is 2/216674.Finally, GCF of Fractions for 8478/262, 8212/827 is 2/216674.