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GCF of 500/523, 406/586

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 500/523, 406/586 i.e 2/306478 easily. The following is the detailed procedure to determine the greatest common factor of fractions 500/523, 406/586.

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 500/523,406/586?

Given fractions are 500/523,406/586

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 500/523,406/586, numerators are 500,406

Denominators are 523,586

The GCF of 500,406 is 2 .

LCM of 523,586 is 306478.

The greatest common factor of 500/523,406/586 = [GCF of 500,406]/[LCM of 523,586]= 2/306478

Therefore, the GCF of 500/523,406/586 is 2/306478.

Greatest Common Factor of 500,406

To find the highest common factor of 500,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 500,406 is 2.

Lets's calculate GCF of 500,406

Greatest Common Factor (GCF) of 500,406 By Common Division

2 500, 406
250, 203

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

Greatest Common Factor of 500,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 500,406 By Matching Biggest Common Factor Method

Now, list down the factors of 500

:

1,2,4,5,10,20,25,50,100,125,250,500

Now, list down the factors of 406

:

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 500,406 . The biggest common factor number is the GCF number.
So the greatest common factor 500,406 is 2.

Lets's calculate LCM of 523,586

Lowest Common Multiple of 523,586 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 306478

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/306478

Therefore, the GCF of Fractions 500/523,406/586 is 2/306478

Least Common Multiple of 523,586 with GCF Formula

Least Common Multiple of 523,586 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 523,586 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(523,586) = 1

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

GCF(523,586) x common factors =1 x 1 = 1

LCM(523,586) = ( 523 × 586 ) / 1

LCM(523,586) = 306478 / 1

LCM(523,586) = 306478


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FAQs on GCF of Fractions of 500/523, 406/586

1. What is the HCF of 500,406?

The HCF of 500,406 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 500/523, 406/586?

Answer: GCF of Numerators as per given numbers 500/523, 406/586 is

GCF of Numerators i.e. for 500,406 is 2

LCM of denominators i.e. for 523,586 is 306478.

Thus, GCF of Fractions is 2/306478.Finally, GCF of Fractions for 500/523, 406/586 is 2/306478.