How to Find GCF of 521/428, 1658/9912?

GCF of 521/428, 1658/9912

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 521/428, 1658/9912 i.e 1/1060584 easily. The following is the detailed procedure to determine the greatest common factor of fractions 521/428, 1658/9912.

Enter two or more fractions separated by "commas"

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

What is the GCF of 521/428,1658/9912?

Given fractions are 521/428,1658/9912

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 521/428,1658/9912, numerators are 521,1658

Denominators are 428,9912

The GCF of 521,1658 is 1 .

LCM of 428,9912 is 1060584.

The greatest common factor of 521/428,1658/9912 = [GCF of 521,1658]/[LCM of 428,9912]= 1/1060584

Therefore, the GCF of 521/428,1658/9912 is 1/1060584.

Greatest Common Factor of 521,1658

To find the highest common factor of 521,1658, we have to find the factors of both numbers and list the highest common factor.

The factors of 521 are 1, 521

The factors of 1658 are 1, 2, 829, 1658

The HCF of 521,1658 is 1.

Lets's calculate GCF of 521,1658

Greatest Common Factor (GCF) of 521,1658 By Common Division

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

Greatest Common Factor of 521,1658 By Matching Biggest Common Factor Method

Now, list down the factors of 521

1,521

Now, list down the factors of 1658

1,2,829,1658

Greatest Common Factor

We found the factors 521,1658 . The biggest common factor number is the GCF number.
So the greatest common factor 521,1658 is 1.

Lets's calculate LCM of 428,9912

Lowest Common Multiple of 428,9912 using Common Division

2	428, 9912
2	214, 4956
	107, 2478

∴ So the LCM of the given numbers is 2 x 2 x 107 x 2478 = 1060584

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1060584

Therefore, the GCF of Fractions 521/428,1658/9912 is 1/1060584

Least Common Multiple of 428,9912 with GCF Formula

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

We need to calculate greatest common factor of 428,9912 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(428,9912) = 4

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

GCF(428,9912) x common factors =4 x 1 = 4

LCM(428,9912) = ( 428 × 9912 ) / 4

LCM(428,9912) = 4242336 / 4

LCM(428,9912) = 1060584

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FAQs on GCF of Fractions of 521/428, 1658/9912

1. What is the HCF of 521,1658?

The HCF of 521,1658 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 521/428, 1658/9912?

Answer: GCF of Numerators as per given numbers 521/428, 1658/9912 is

GCF of Numerators i.e. for 521,1658 is 1

LCM of denominators i.e. for 428,9912 is 1060584.

Thus, GCF of Fractions is 1/1060584.Finally, GCF of Fractions for 521/428, 1658/9912 is 1/1060584.