How to Find GCF of 7734/173, 7278/2246?

GCF of 7734/173, 7278/2246

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 7734/173, 7278/2246 i.e 6/388558 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7734/173, 7278/2246.

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 7734/173,7278/2246?

Given fractions are 7734/173,7278/2246

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 7734/173,7278/2246, numerators are 7734,7278

Denominators are 173,2246

The GCF of 7734,7278 is 6 .

LCM of 173,2246 is 388558.

The greatest common factor of 7734/173,7278/2246 = [GCF of 7734,7278]/[LCM of 173,2246]= 6/388558

Therefore, the GCF of 7734/173,7278/2246 is 6/388558.

Greatest Common Factor of 7734,7278

To find the highest common factor of 7734,7278, we have to find the factors of both numbers and list the highest common factor.

The factors of 7734 are 1, 2, 3, 6, 1289, 2578, 3867, 7734

The factors of 7278 are 1, 2, 3, 6, 1213, 2426, 3639, 7278

The HCF of 7734,7278 is 6.

Lets's calculate GCF of 7734,7278

Greatest Common Factor (GCF) of 7734,7278 By Common Division

2	7734, 7278
3	3867, 3639
	1289, 1213

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 7734,7278 By Matching Biggest Common Factor Method

Now, list down the factors of 7734

1,2,3,6,1289,2578,3867,7734

Now, list down the factors of 7278

1,2,3,6,1213,2426,3639,7278

Greatest Common Factor

We found the factors 7734,7278 . The biggest common factor number is the GCF number.
So the greatest common factor 7734,7278 is 6.

Lets's calculate LCM of 173,2246

Lowest Common Multiple of 173,2246 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 388558

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/388558

Therefore, the GCF of Fractions 7734/173,7278/2246 is 6/388558

Least Common Multiple of 173,2246 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 173,2246 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(173,2246) = 1

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

GCF(173,2246) x common factors =1 x 1 = 1

LCM(173,2246) = ( 173 × 2246 ) / 1

LCM(173,2246) = 388558 / 1

LCM(173,2246) = 388558

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 7734/173, 7278/2246

1. What is the HCF of 7734,7278?

The HCF of 7734,7278 is 6

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 7734/173, 7278/2246?

Answer: GCF of Numerators as per given numbers 7734/173, 7278/2246 is

GCF of Numerators i.e. for 7734,7278 is 6

LCM of denominators i.e. for 173,2246 is 388558.

Thus, GCF of Fractions is 6/388558.Finally, GCF of Fractions for 7734/173, 7278/2246 is 6/388558.