How to Find GCF of 12/905, 10/746, 782/812?

GCF of 12/905, 10/746, 782/812

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 12/905, 10/746, 782/812 i.e 2/274102780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 12/905, 10/746, 782/812.

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 12/905,10/746,782/812?

Given fractions are 12/905,10/746,782/812

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 12/905,10/746,782/812, numerators are 12,10,782

Denominators are 905,746,812

The GCF of 12,10,782 is 2 .

LCM of 905,746,812 is 274102780.

The greatest common factor of 12/905,10/746,782/812 = [GCF of 12,10,782]/[LCM of 905,746,812]= 2/274102780

Therefore, the GCF of 12/905,10/746,782/812 is 2/274102780.

Greatest Common Factor of 12,10,782

To find the highest common factor of 12,10,782, we have to find the factors of both numbers and list the highest common factor.

The factors of 12 are 1, 2, 3, 4, 6, 12

The factors of 10 are 1, 2, 5, 10

The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782

The HCF of 12,10,782 is 2.

Lets's calculate GCF of 12,10,782

Greatest Common Factor (GCF) of 12,10,782 By Common Division

2	12, 10, 782
	6, 5, 391

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

Greatest Common Factor of 12,10,782 By Matching Biggest Common Factor Method

Now, list down the factors of 12

1,2,3,4,6,12

Now, list down the factors of 10

1,2,5,10

Now, list down the factors of 782

1,2,17,23,34,46,391,782

Greatest Common Factor

We found the factors 12,10,782 . The biggest common factor number is the GCF number.
So the greatest common factor 12,10,782 is 2.

Lets's calculate LCM of 905,746,812

Lowest Common Multiple of 905,746,812 using Common Division

2	905, 746, 812
	905, 373, 406

∴ So the LCM of the given numbers is 2 x 905 x 373 x 406 = 274102780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/274102780

Therefore, the GCF of Fractions 12/905,10/746,782/812 is 2/274102780

Least Common Multiple of 905,746,812 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 905,746,812 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(905,746,812) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(905,746,812) x common factors =1 x 2 = 2

LCM(905,746,812) = ( 905 × 746 × 812 ) / 2

LCM(905,746,812) = 548205560 / 2

LCM(905,746,812) = 274102780

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 12/905, 10/746, 782/812

1. What is the HCF of 12,10,782?

The HCF of 12,10,782 is 2

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 12/905, 10/746, 782/812?

Answer: GCF of Numerators as per given numbers 12/905, 10/746, 782/812 is

GCF of Numerators i.e. for 12,10,782 is 2

LCM of denominators i.e. for 905,746,812 is 274102780.

Thus, GCF of Fractions is 2/274102780.Finally, GCF of Fractions for 12/905, 10/746, 782/812 is 2/274102780.