How to Find GCF of 540/92, 768/820?

GCF of 540/92, 768/820

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 540/92, 768/820 i.e 12/18860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/92, 768/820.

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 540/92,768/820?

Given fractions are 540/92,768/820

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 540/92,768/820, numerators are 540,768

Denominators are 92,820

The GCF of 540,768 is 12 .

LCM of 92,820 is 18860.

The greatest common factor of 540/92,768/820 = [GCF of 540,768]/[LCM of 92,820]= 12/18860

Therefore, the GCF of 540/92,768/820 is 12/18860.

Greatest Common Factor of 540,768

To find the highest common factor of 540,768, we have to find the factors of both numbers and list the highest common factor.

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 factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768

The HCF of 540,768 is 12.

Lets's calculate GCF of 540,768

Greatest Common Factor (GCF) of 540,768 By Common Division

2	540, 768
2	270, 384
3	135, 192
	45, 64

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 540,768 By Matching Biggest Common Factor Method

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

Now, list down the factors of 768

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768

Greatest Common Factor

We found the factors 540,768 . The biggest common factor number is the GCF number.
So the greatest common factor 540,768 is 12.

Lets's calculate LCM of 92,820

Lowest Common Multiple of 92,820 using Common Division

2	92, 820
2	46, 410
	23, 205

∴ So the LCM of the given numbers is 2 x 2 x 23 x 205 = 18860

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/18860

Therefore, the GCF of Fractions 540/92,768/820 is 12/18860

Least Common Multiple of 92,820 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 92,820 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(92,820) = 4

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

GCF(92,820) x common factors =4 x 1 = 4

LCM(92,820) = ( 92 × 820 ) / 4

LCM(92,820) = 75440 / 4

LCM(92,820) = 18860

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FAQs on GCF of Fractions of 540/92, 768/820

1. What is the HCF of 540,768?

The HCF of 540,768 is 12

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 540/92, 768/820?

Answer: GCF of Numerators as per given numbers 540/92, 768/820 is

GCF of Numerators i.e. for 540,768 is 12

LCM of denominators i.e. for 92,820 is 18860.

Thus, GCF of Fractions is 12/18860.Finally, GCF of Fractions for 540/92, 768/820 is 12/18860.