How to Find GCF of 2409/608, 2778/9172?

GCF of 2409/608, 2778/9172

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 2409/608, 2778/9172 i.e 3/1394144 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2409/608, 2778/9172.

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 2409/608,2778/9172?

Given fractions are 2409/608,2778/9172

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 2409/608,2778/9172, numerators are 2409,2778

Denominators are 608,9172

The GCF of 2409,2778 is 3 .

LCM of 608,9172 is 1394144.

The greatest common factor of 2409/608,2778/9172 = [GCF of 2409,2778]/[LCM of 608,9172]= 3/1394144

Therefore, the GCF of 2409/608,2778/9172 is 3/1394144.

Greatest Common Factor of 2409,2778

To find the highest common factor of 2409,2778, we have to find the factors of both numbers and list the highest common factor.

The factors of 2409 are 1, 3, 11, 33, 73, 219, 803, 2409

The factors of 2778 are 1, 2, 3, 6, 463, 926, 1389, 2778

The HCF of 2409,2778 is 3.

Lets's calculate GCF of 2409,2778

Greatest Common Factor (GCF) of 2409,2778 By Common Division

3	2409, 2778
	803, 926

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 2409,2778 By Matching Biggest Common Factor Method

Now, list down the factors of 2409

1,3,11,33,73,219,803,2409

Now, list down the factors of 2778

1,2,3,6,463,926,1389,2778

Greatest Common Factor

We found the factors 2409,2778 . The biggest common factor number is the GCF number.
So the greatest common factor 2409,2778 is 3.

Lets's calculate LCM of 608,9172

Lowest Common Multiple of 608,9172 using Common Division

2	608, 9172
2	304, 4586
	152, 2293

∴ So the LCM of the given numbers is 2 x 2 x 152 x 2293 = 1394144

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1394144

Therefore, the GCF of Fractions 2409/608,2778/9172 is 3/1394144

Least Common Multiple of 608,9172 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 608,9172 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(608,9172) = 4

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

GCF(608,9172) x common factors =4 x 1 = 4

LCM(608,9172) = ( 608 × 9172 ) / 4

LCM(608,9172) = 5576576 / 4

LCM(608,9172) = 1394144

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FAQs on GCF of Fractions of 2409/608, 2778/9172

1. What is the HCF of 2409,2778?

The HCF of 2409,2778 is 3

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 2409/608, 2778/9172?

Answer: GCF of Numerators as per given numbers 2409/608, 2778/9172 is

GCF of Numerators i.e. for 2409,2778 is 3

LCM of denominators i.e. for 608,9172 is 1394144.

Thus, GCF of Fractions is 3/1394144.Finally, GCF of Fractions for 2409/608, 2778/9172 is 3/1394144.