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GCF of 421/314, 470/688

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 421/314, 470/688 i.e 1/108016 easily. The following is the detailed procedure to determine the greatest common factor of fractions 421/314, 470/688.

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 421/314,470/688?

Given fractions are 421/314,470/688

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 421/314,470/688, numerators are 421,470

Denominators are 314,688

The GCF of 421,470 is 1 .

LCM of 314,688 is 108016.

The greatest common factor of 421/314,470/688 = [GCF of 421,470]/[LCM of 314,688]= 1/108016

Therefore, the GCF of 421/314,470/688 is 1/108016.

Greatest Common Factor of 421,470

To find the highest common factor of 421,470, we have to find the factors of both numbers and list the highest common factor.

The factors of 421 are 1, 421

The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470

The HCF of 421,470 is 1.

Lets's calculate GCF of 421,470

Greatest Common Factor (GCF) of 421,470 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 421,470 By Matching Biggest Common Factor Method

Greatest Common Factor of 421,470 By Matching Biggest Common Factor Method

Now, list down the factors of 421

:

1,421

Now, list down the factors of 470

:

1,2,5,10,47,94,235,470

Greatest Common Factor

We found the factors 421,470 . The biggest common factor number is the GCF number.
So the greatest common factor 421,470 is 1.

Lets's calculate LCM of 314,688

Lowest Common Multiple of 314,688 using Common Division

2 314, 688
157, 344

∴ So the LCM of the given numbers is 2 x 157 x 344 = 108016

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/108016

Therefore, the GCF of Fractions 421/314,470/688 is 1/108016

Least Common Multiple of 314,688 with GCF Formula

Least Common Multiple of 314,688 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 314,688 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,688) = 2

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

GCF(314,688) x common factors =2 x 1 = 2

LCM(314,688) = ( 314 × 688 ) / 2

LCM(314,688) = 216032 / 2

LCM(314,688) = 108016


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FAQs on GCF of Fractions of 421/314, 470/688

1. What is the HCF of 421,470?

The HCF of 421,470 is 1

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 421/314, 470/688?

Answer: GCF of Numerators as per given numbers 421/314, 470/688 is

GCF of Numerators i.e. for 421,470 is 1

LCM of denominators i.e. for 314,688 is 108016.

Thus, GCF of Fractions is 1/108016.Finally, GCF of Fractions for 421/314, 470/688 is 1/108016.