How to Find GCF of 520/67, 540/677?

GCF of 520/67, 540/677

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 520/67, 540/677 i.e 20/45359 easily. The following is the detailed procedure to determine the greatest common factor of fractions 520/67, 540/677.

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 520/67,540/677?

Given fractions are 520/67,540/677

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 520/67,540/677, numerators are 520,540

Denominators are 67,677

The GCF of 520,540 is 20 .

LCM of 67,677 is 45359.

The greatest common factor of 520/67,540/677 = [GCF of 520,540]/[LCM of 67,677]= 20/45359

Therefore, the GCF of 520/67,540/677 is 20/45359.

Greatest Common Factor of 520,540

To find the highest common factor of 520,540, we have to find the factors of both numbers and list the highest common factor.

The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520

The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

The HCF of 520,540 is 20.

Lets's calculate GCF of 520,540

Greatest Common Factor (GCF) of 520,540 By Common Division

2	520, 540
2	260, 270
5	130, 135
	26, 27

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 520,540 By Matching Biggest Common Factor Method

Now, list down the factors of 520

1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520

Now, list down the factors of 540

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Greatest Common Factor

We found the factors 520,540 . The biggest common factor number is the GCF number.
So the greatest common factor 520,540 is 20.

Lets's calculate LCM of 67,677

Lowest Common Multiple of 67,677 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 45359

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/45359

Therefore, the GCF of Fractions 520/67,540/677 is 20/45359

Least Common Multiple of 67,677 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 67,677 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(67,677) = 1

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

GCF(67,677) x common factors =1 x 1 = 1

LCM(67,677) = ( 67 × 677 ) / 1

LCM(67,677) = 45359 / 1

LCM(67,677) = 45359

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FAQs on GCF of Fractions of 520/67, 540/677

1. What is the HCF of 520,540?

The HCF of 520,540 is 20

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 520/67, 540/677?

Answer: GCF of Numerators as per given numbers 520/67, 540/677 is

GCF of Numerators i.e. for 520,540 is 20

LCM of denominators i.e. for 67,677 is 45359.

Thus, GCF of Fractions is 20/45359.Finally, GCF of Fractions for 520/67, 540/677 is 20/45359.