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GCF of 164/55, 902/686

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 164/55, 902/686 i.e 82/37730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 164/55, 902/686.

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 164/55,902/686?

Given fractions are 164/55,902/686

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 164/55,902/686, numerators are 164,902

Denominators are 55,686

The GCF of 164,902 is 82 .

LCM of 55,686 is 37730.

The greatest common factor of 164/55,902/686 = [GCF of 164,902]/[LCM of 55,686]= 82/37730

Therefore, the GCF of 164/55,902/686 is 82/37730.

Greatest Common Factor of 164,902

To find the highest common factor of 164,902, we have to find the factors of both numbers and list the highest common factor.

The factors of 164 are 1, 2, 4, 41, 82, 164

The factors of 902 are 1, 2, 11, 22, 41, 82, 451, 902

The HCF of 164,902 is 82.

Lets's calculate GCF of 164,902

Greatest Common Factor (GCF) of 164,902 By Common Division

2 164, 902
41 82, 451
2, 11

∴ So the GCF of the given numbers is 2 x 41 = 82

Greatest Common Factor of 164,902 By Matching Biggest Common Factor Method

Greatest Common Factor of 164,902 By Matching Biggest Common Factor Method

Now, list down the factors of 164

:

1,2,4,41,82,164

Now, list down the factors of 902

:

1,2,11,22,41,82,451,902

Greatest Common Factor

We found the factors 164,902 . The biggest common factor number is the GCF number.
So the greatest common factor 164,902 is 82.

Lets's calculate LCM of 55,686

Lowest Common Multiple of 55,686 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 37730

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 82/37730

Therefore, the GCF of Fractions 164/55,902/686 is 82/37730

Least Common Multiple of 55,686 with GCF Formula

Least Common Multiple of 55,686 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 55,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(55,686) = 1

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

GCF(55,686) x common factors =1 x 1 = 1

LCM(55,686) = ( 55 × 686 ) / 1

LCM(55,686) = 37730 / 1

LCM(55,686) = 37730


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FAQs on GCF of Fractions of 164/55, 902/686

1. What is the HCF of 164,902?

The HCF of 164,902 is 82

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 164/55, 902/686?

Answer: GCF of Numerators as per given numbers 164/55, 902/686 is

GCF of Numerators i.e. for 164,902 is 82

LCM of denominators i.e. for 55,686 is 37730.

Thus, GCF of Fractions is 82/37730.Finally, GCF of Fractions for 164/55, 902/686 is 82/37730.