How to Find GCF of 8274/289, 5128/9177?

GCF of 8274/289, 5128/9177

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 8274/289, 5128/9177 i.e 2/2652153 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8274/289, 5128/9177.

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 8274/289,5128/9177?

Given fractions are 8274/289,5128/9177

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 8274/289,5128/9177, numerators are 8274,5128

Denominators are 289,9177

The GCF of 8274,5128 is 2 .

LCM of 289,9177 is 2652153.

The greatest common factor of 8274/289,5128/9177 = [GCF of 8274,5128]/[LCM of 289,9177]= 2/2652153

Therefore, the GCF of 8274/289,5128/9177 is 2/2652153.

Greatest Common Factor of 8274,5128

To find the highest common factor of 8274,5128, we have to find the factors of both numbers and list the highest common factor.

The factors of 8274 are 1, 2, 3, 6, 7, 14, 21, 42, 197, 394, 591, 1182, 1379, 2758, 4137, 8274

The factors of 5128 are 1, 2, 4, 8, 641, 1282, 2564, 5128

The HCF of 8274,5128 is 2.

Lets's calculate GCF of 8274,5128

Greatest Common Factor (GCF) of 8274,5128 By Common Division

2	8274, 5128
	4137, 2564

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

Greatest Common Factor of 8274,5128 By Matching Biggest Common Factor Method

Now, list down the factors of 8274

1,2,3,6,7,14,21,42,197,394,591,1182,1379,2758,4137,8274

Now, list down the factors of 5128

1,2,4,8,641,1282,2564,5128

Greatest Common Factor

We found the factors 8274,5128 . The biggest common factor number is the GCF number.
So the greatest common factor 8274,5128 is 2.

Lets's calculate LCM of 289,9177

Lowest Common Multiple of 289,9177 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2652153

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2652153

Therefore, the GCF of Fractions 8274/289,5128/9177 is 2/2652153

Least Common Multiple of 289,9177 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 289,9177 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,9177) = 1

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

GCF(289,9177) x common factors =1 x 1 = 1

LCM(289,9177) = ( 289 × 9177 ) / 1

LCM(289,9177) = 2652153 / 1

LCM(289,9177) = 2652153

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 8274/289, 5128/9177

1. What is the HCF of 8274,5128?

The HCF of 8274,5128 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 8274/289, 5128/9177?

Answer: GCF of Numerators as per given numbers 8274/289, 5128/9177 is

GCF of Numerators i.e. for 8274,5128 is 2

LCM of denominators i.e. for 289,9177 is 2652153.

Thus, GCF of Fractions is 2/2652153.Finally, GCF of Fractions for 8274/289, 5128/9177 is 2/2652153.