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GCF of 821/520, 213/548

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 821/520, 213/548 i.e 1/71240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 821/520, 213/548.

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 821/520,213/548?

Given fractions are 821/520,213/548

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 821/520,213/548, numerators are 821,213

Denominators are 520,548

The GCF of 821,213 is 1 .

LCM of 520,548 is 71240.

The greatest common factor of 821/520,213/548 = [GCF of 821,213]/[LCM of 520,548]= 1/71240

Therefore, the GCF of 821/520,213/548 is 1/71240.

Greatest Common Factor of 821,213

To find the highest common factor of 821,213, we have to find the factors of both numbers and list the highest common factor.

The factors of 821 are 1, 821

The factors of 213 are 1, 3, 71, 213

The HCF of 821,213 is 1.

Lets's calculate GCF of 821,213

Greatest Common Factor (GCF) of 821,213 By Common Division

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

Greatest Common Factor of 821,213 By Matching Biggest Common Factor Method

Greatest Common Factor of 821,213 By Matching Biggest Common Factor Method

Now, list down the factors of 821

:

1,821

Now, list down the factors of 213

:

1,3,71,213

Greatest Common Factor

We found the factors 821,213 . The biggest common factor number is the GCF number.
So the greatest common factor 821,213 is 1.

Lets's calculate LCM of 520,548

Lowest Common Multiple of 520,548 using Common Division

2 520, 548
2 260, 274
130, 137

∴ So the LCM of the given numbers is 2 x 2 x 130 x 137 = 71240

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/71240

Therefore, the GCF of Fractions 821/520,213/548 is 1/71240

Least Common Multiple of 520,548 with GCF Formula

Least Common Multiple of 520,548 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 520,548 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(520,548) = 4

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

GCF(520,548) x common factors =4 x 1 = 4

LCM(520,548) = ( 520 × 548 ) / 4

LCM(520,548) = 284960 / 4

LCM(520,548) = 71240


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FAQs on GCF of Fractions of 821/520, 213/548

1. What is the HCF of 821,213?

The HCF of 821,213 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 821/520, 213/548?

Answer: GCF of Numerators as per given numbers 821/520, 213/548 is

GCF of Numerators i.e. for 821,213 is 1

LCM of denominators i.e. for 520,548 is 71240.

Thus, GCF of Fractions is 1/71240.Finally, GCF of Fractions for 821/520, 213/548 is 1/71240.