How to Find GCF of 506/20, 627/7569?

GCF of 506/20, 627/7569

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 506/20, 627/7569 i.e 11/151380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 506/20, 627/7569.

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 506/20,627/7569?

Given fractions are 506/20,627/7569

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 506/20,627/7569, numerators are 506,627

Denominators are 20,7569

The GCF of 506,627 is 11 .

LCM of 20,7569 is 151380.

The greatest common factor of 506/20,627/7569 = [GCF of 506,627]/[LCM of 20,7569]= 11/151380

Therefore, the GCF of 506/20,627/7569 is 11/151380.

Greatest Common Factor of 506,627

To find the highest common factor of 506,627, we have to find the factors of both numbers and list the highest common factor.

The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506

The factors of 627 are 1, 3, 11, 19, 33, 57, 209, 627

The HCF of 506,627 is 11.

Lets's calculate GCF of 506,627

Greatest Common Factor (GCF) of 506,627 By Common Division

11	506, 627
	46, 57

∴ So the GCF of the given numbers is 11 = 11

Greatest Common Factor of 506,627 By Matching Biggest Common Factor Method

Now, list down the factors of 506

1,2,11,22,23,46,253,506

Now, list down the factors of 627

1,3,11,19,33,57,209,627

Greatest Common Factor

We found the factors 506,627 . The biggest common factor number is the GCF number.
So the greatest common factor 506,627 is 11.

Lets's calculate LCM of 20,7569

Lowest Common Multiple of 20,7569 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 151380

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/151380

Therefore, the GCF of Fractions 506/20,627/7569 is 11/151380

Least Common Multiple of 20,7569 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 20,7569 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,7569) = 1

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

GCF(20,7569) x common factors =1 x 1 = 1

LCM(20,7569) = ( 20 × 7569 ) / 1

LCM(20,7569) = 151380 / 1

LCM(20,7569) = 151380

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FAQs on GCF of Fractions of 506/20, 627/7569

1. What is the HCF of 506,627?

The HCF of 506,627 is 11

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 506/20, 627/7569?

Answer: GCF of Numerators as per given numbers 506/20, 627/7569 is

GCF of Numerators i.e. for 506,627 is 11

LCM of denominators i.e. for 20,7569 is 151380.

Thus, GCF of Fractions is 11/151380.Finally, GCF of Fractions for 506/20, 627/7569 is 11/151380.