How to Find GCF of 1994/775, 1416/1306?

GCF of 1994/775, 1416/1306

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 1994/775, 1416/1306 i.e 2/1012150 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1994/775, 1416/1306.

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 1994/775,1416/1306?

Given fractions are 1994/775,1416/1306

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 1994/775,1416/1306, numerators are 1994,1416

Denominators are 775,1306

The GCF of 1994,1416 is 2 .

LCM of 775,1306 is 1012150.

The greatest common factor of 1994/775,1416/1306 = [GCF of 1994,1416]/[LCM of 775,1306]= 2/1012150

Therefore, the GCF of 1994/775,1416/1306 is 2/1012150.

Greatest Common Factor of 1994,1416

To find the highest common factor of 1994,1416, we have to find the factors of both numbers and list the highest common factor.

The factors of 1994 are 1, 2, 997, 1994

The factors of 1416 are 1, 2, 3, 4, 6, 8, 12, 24, 59, 118, 177, 236, 354, 472, 708, 1416

The HCF of 1994,1416 is 2.

Lets's calculate GCF of 1994,1416

Greatest Common Factor (GCF) of 1994,1416 By Common Division

2	1994, 1416
	997, 708

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

Greatest Common Factor of 1994,1416 By Matching Biggest Common Factor Method

Now, list down the factors of 1994

1,2,997,1994

Now, list down the factors of 1416

1,2,3,4,6,8,12,24,59,118,177,236,354,472,708,1416

Greatest Common Factor

We found the factors 1994,1416 . The biggest common factor number is the GCF number.
So the greatest common factor 1994,1416 is 2.

Lets's calculate LCM of 775,1306

Lowest Common Multiple of 775,1306 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1012150

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1012150

Therefore, the GCF of Fractions 1994/775,1416/1306 is 2/1012150

Least Common Multiple of 775,1306 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 775,1306 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(775,1306) = 1

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

GCF(775,1306) x common factors =1 x 1 = 1

LCM(775,1306) = ( 775 × 1306 ) / 1

LCM(775,1306) = 1012150 / 1

LCM(775,1306) = 1012150

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 1994/775, 1416/1306

1. What is the HCF of 1994,1416?

The HCF of 1994,1416 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 1994/775, 1416/1306?

Answer: GCF of Numerators as per given numbers 1994/775, 1416/1306 is

GCF of Numerators i.e. for 1994,1416 is 2

LCM of denominators i.e. for 775,1306 is 1012150.

Thus, GCF of Fractions is 2/1012150.Finally, GCF of Fractions for 1994/775, 1416/1306 is 2/1012150.