How to Find GCF of 428/190, 540/526?

GCF of 428/190, 540/526

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 428/190, 540/526 i.e 4/49970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 428/190, 540/526.

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 428/190,540/526?

Given fractions are 428/190,540/526

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 428/190,540/526, numerators are 428,540

Denominators are 190,526

The GCF of 428,540 is 4 .

LCM of 190,526 is 49970.

The greatest common factor of 428/190,540/526 = [GCF of 428,540]/[LCM of 190,526]= 4/49970

Therefore, the GCF of 428/190,540/526 is 4/49970.

Greatest Common Factor of 428,540

To find the highest common factor of 428,540, we have to find the factors of both numbers and list the highest common factor.

The factors of 428 are 1, 2, 4, 107, 214, 428

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 428,540 is 4.

Lets's calculate GCF of 428,540

Greatest Common Factor (GCF) of 428,540 By Common Division

2	428, 540
2	214, 270
	107, 135

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 428,540 By Matching Biggest Common Factor Method

Now, list down the factors of 428

1,2,4,107,214,428

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 428,540 . The biggest common factor number is the GCF number.
So the greatest common factor 428,540 is 4.

Lets's calculate LCM of 190,526

Lowest Common Multiple of 190,526 using Common Division

2	190, 526
	95, 263

∴ So the LCM of the given numbers is 2 x 95 x 263 = 49970

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/49970

Therefore, the GCF of Fractions 428/190,540/526 is 4/49970

Least Common Multiple of 190,526 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 190,526 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(190,526) = 2

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

GCF(190,526) x common factors =2 x 1 = 2

LCM(190,526) = ( 190 × 526 ) / 2

LCM(190,526) = 99940 / 2

LCM(190,526) = 49970

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FAQs on GCF of Fractions of 428/190, 540/526

1. What is the HCF of 428,540?

The HCF of 428,540 is 4

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 428/190, 540/526?

Answer: GCF of Numerators as per given numbers 428/190, 540/526 is

GCF of Numerators i.e. for 428,540 is 4

LCM of denominators i.e. for 190,526 is 49970.

Thus, GCF of Fractions is 4/49970.Finally, GCF of Fractions for 428/190, 540/526 is 4/49970.