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GCF of 812/64, 442/209

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 812/64, 442/209 i.e 2/13376 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/64, 442/209.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 812/64,442/209?

Given fractions are 812/64,442/209

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 812/64,442/209, numerators are 812,442

Denominators are 64,209

The GCF of 812,442 is 2 .

LCM of 64,209 is 13376.

The greatest common factor of 812/64,442/209 = [GCF of 812,442]/[LCM of 64,209]= 2/13376

Therefore, the GCF of 812/64,442/209 is 2/13376.

Greatest Common Factor of 812,442

To find the highest common factor of 812,442, we have to find the factors of both numbers and list the highest common factor.

The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812

The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442

The HCF of 812,442 is 2.

Lets's calculate GCF of 812,442

Greatest Common Factor (GCF) of 812,442 By Common Division

2 812, 442
406, 221

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

Greatest Common Factor of 812,442 By Matching Biggest Common Factor Method

Greatest Common Factor of 812,442 By Matching Biggest Common Factor Method

Now, list down the factors of 812

:

1,2,4,7,14,28,29,58,116,203,406,812

Now, list down the factors of 442

:

1,2,13,17,26,34,221,442

Greatest Common Factor

We found the factors 812,442 . The biggest common factor number is the GCF number.
So the greatest common factor 812,442 is 2.

Lets's calculate LCM of 64,209

Lowest Common Multiple of 64,209 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 13376

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/13376

Therefore, the GCF of Fractions 812/64,442/209 is 2/13376

Least Common Multiple of 64,209 with GCF Formula

Least Common Multiple of 64,209 with GCF Formula

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

We need to calculate greatest common factor of 64,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(64,209) = 1

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

GCF(64,209) x common factors =1 x 1 = 1

LCM(64,209) = ( 64 × 209 ) / 1

LCM(64,209) = 13376 / 1

LCM(64,209) = 13376


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FAQs on GCF of Fractions of 812/64, 442/209

1. What is the HCF of 812,442?

The HCF of 812,442 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 812/64, 442/209?

Answer: GCF of Numerators as per given numbers 812/64, 442/209 is

GCF of Numerators i.e. for 812,442 is 2

LCM of denominators i.e. for 64,209 is 13376.

Thus, GCF of Fractions is 2/13376.Finally, GCF of Fractions for 812/64, 442/209 is 2/13376.