How to Find GCF of 420/382, 503/592?

GCF of 420/382, 503/592

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 420/382, 503/592 i.e 1/113072 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/382, 503/592.

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 420/382,503/592?

Given fractions are 420/382,503/592

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 420/382,503/592, numerators are 420,503

Denominators are 382,592

The GCF of 420,503 is 1 .

LCM of 382,592 is 113072.

The greatest common factor of 420/382,503/592 = [GCF of 420,503]/[LCM of 382,592]= 1/113072

Therefore, the GCF of 420/382,503/592 is 1/113072.

Greatest Common Factor of 420,503

To find the highest common factor of 420,503, we have to find the factors of both numbers and list the highest common factor.

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

The factors of 503 are 1, 503

The HCF of 420,503 is 1.

Lets's calculate GCF of 420,503

Greatest Common Factor (GCF) of 420,503 By Common Division

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

Greatest Common Factor of 420,503 By Matching Biggest Common Factor Method

Now, list down the factors of 420

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Now, list down the factors of 503

1,503

Greatest Common Factor

We found the factors 420,503 . The biggest common factor number is the GCF number.
So the greatest common factor 420,503 is 1.

Lets's calculate LCM of 382,592

Lowest Common Multiple of 382,592 using Common Division

2	382, 592
	191, 296

∴ So the LCM of the given numbers is 2 x 191 x 296 = 113072

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/113072

Therefore, the GCF of Fractions 420/382,503/592 is 1/113072

Least Common Multiple of 382,592 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 382,592 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(382,592) = 2

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

GCF(382,592) x common factors =2 x 1 = 2

LCM(382,592) = ( 382 × 592 ) / 2

LCM(382,592) = 226144 / 2

LCM(382,592) = 113072

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FAQs on GCF of Fractions of 420/382, 503/592

1. What is the HCF of 420,503?

The HCF of 420,503 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 420/382, 503/592?

Answer: GCF of Numerators as per given numbers 420/382, 503/592 is

GCF of Numerators i.e. for 420,503 is 1

LCM of denominators i.e. for 382,592 is 113072.

Thus, GCF of Fractions is 1/113072.Finally, GCF of Fractions for 420/382, 503/592 is 1/113072.