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GCF of 286/275, 1022/218

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 286/275, 1022/218 i.e 2/59950 easily. The following is the detailed procedure to determine the greatest common factor of fractions 286/275, 1022/218.

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 286/275,1022/218?

Given fractions are 286/275,1022/218

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 286/275,1022/218, numerators are 286,1022

Denominators are 275,218

The GCF of 286,1022 is 2 .

LCM of 275,218 is 59950.

The greatest common factor of 286/275,1022/218 = [GCF of 286,1022]/[LCM of 275,218]= 2/59950

Therefore, the GCF of 286/275,1022/218 is 2/59950.

Greatest Common Factor of 286,1022

To find the highest common factor of 286,1022, we have to find the factors of both numbers and list the highest common factor.

The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286

The factors of 1022 are 1, 2, 7, 14, 73, 146, 511, 1022

The HCF of 286,1022 is 2.

Lets's calculate GCF of 286,1022

Greatest Common Factor (GCF) of 286,1022 By Common Division

2 286, 1022
143, 511

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

Greatest Common Factor of 286,1022 By Matching Biggest Common Factor Method

Greatest Common Factor of 286,1022 By Matching Biggest Common Factor Method

Now, list down the factors of 286

:

1,2,11,13,22,26,143,286

Now, list down the factors of 1022

:

1,2,7,14,73,146,511,1022

Greatest Common Factor

We found the factors 286,1022 . The biggest common factor number is the GCF number.
So the greatest common factor 286,1022 is 2.

Lets's calculate LCM of 275,218

Lowest Common Multiple of 275,218 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 59950

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/59950

Therefore, the GCF of Fractions 286/275,1022/218 is 2/59950

Least Common Multiple of 275,218 with GCF Formula

Least Common Multiple of 275,218 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 275,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(275,218) = 1

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

GCF(275,218) x common factors =1 x 1 = 1

LCM(275,218) = ( 275 × 218 ) / 1

LCM(275,218) = 59950 / 1

LCM(275,218) = 59950


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FAQs on GCF of Fractions of 286/275, 1022/218

1. What is the HCF of 286,1022?

The HCF of 286,1022 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 286/275, 1022/218?

Answer: GCF of Numerators as per given numbers 286/275, 1022/218 is

GCF of Numerators i.e. for 286,1022 is 2

LCM of denominators i.e. for 275,218 is 59950.

Thus, GCF of Fractions is 2/59950.Finally, GCF of Fractions for 286/275, 1022/218 is 2/59950.