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GCF of 206/310, 112/422

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 206/310, 112/422 i.e 2/65410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 206/310, 112/422.

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 206/310,112/422?

Given fractions are 206/310,112/422

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 206/310,112/422, numerators are 206,112

Denominators are 310,422

The GCF of 206,112 is 2 .

LCM of 310,422 is 65410.

The greatest common factor of 206/310,112/422 = [GCF of 206,112]/[LCM of 310,422]= 2/65410

Therefore, the GCF of 206/310,112/422 is 2/65410.

Greatest Common Factor of 206,112

To find the highest common factor of 206,112, we have to find the factors of both numbers and list the highest common factor.

The factors of 206 are 1, 2, 103, 206

The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

The HCF of 206,112 is 2.

Lets's calculate GCF of 206,112

Greatest Common Factor (GCF) of 206,112 By Common Division

2 206, 112
103, 56

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

Greatest Common Factor of 206,112 By Matching Biggest Common Factor Method

Greatest Common Factor of 206,112 By Matching Biggest Common Factor Method

Now, list down the factors of 206

:

1,2,103,206

Now, list down the factors of 112

:

1,2,4,7,8,14,16,28,56,112

Greatest Common Factor

We found the factors 206,112 . The biggest common factor number is the GCF number.
So the greatest common factor 206,112 is 2.

Lets's calculate LCM of 310,422

Lowest Common Multiple of 310,422 using Common Division

2 310, 422
155, 211

∴ So the LCM of the given numbers is 2 x 155 x 211 = 65410

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/65410

Therefore, the GCF of Fractions 206/310,112/422 is 2/65410

Least Common Multiple of 310,422 with GCF Formula

Least Common Multiple of 310,422 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 310,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(310,422) = 2

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

GCF(310,422) x common factors =2 x 1 = 2

LCM(310,422) = ( 310 × 422 ) / 2

LCM(310,422) = 130820 / 2

LCM(310,422) = 65410


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FAQs on GCF of Fractions of 206/310, 112/422

1. What is the HCF of 206,112?

The HCF of 206,112 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 206/310, 112/422?

Answer: GCF of Numerators as per given numbers 206/310, 112/422 is

GCF of Numerators i.e. for 206,112 is 2

LCM of denominators i.e. for 310,422 is 65410.

Thus, GCF of Fractions is 2/65410.Finally, GCF of Fractions for 206/310, 112/422 is 2/65410.