How to Find GCF of 2609/688, 1138/408?

GCF of 2609/688, 1138/408

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 2609/688, 1138/408 i.e 1/35088 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2609/688, 1138/408.

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 2609/688,1138/408?

Given fractions are 2609/688,1138/408

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 2609/688,1138/408, numerators are 2609,1138

Denominators are 688,408

The GCF of 2609,1138 is 1 .

LCM of 688,408 is 35088.

The greatest common factor of 2609/688,1138/408 = [GCF of 2609,1138]/[LCM of 688,408]= 1/35088

Therefore, the GCF of 2609/688,1138/408 is 1/35088.

Greatest Common Factor of 2609,1138

To find the highest common factor of 2609,1138, we have to find the factors of both numbers and list the highest common factor.

The factors of 2609 are 1, 2609

The factors of 1138 are 1, 2, 569, 1138

The HCF of 2609,1138 is 1.

Lets's calculate GCF of 2609,1138

Greatest Common Factor (GCF) of 2609,1138 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 2609,1138 By Matching Biggest Common Factor Method

Now, list down the factors of 2609

1,2609

Now, list down the factors of 1138

1,2,569,1138

Greatest Common Factor

We found the factors 2609,1138 . The biggest common factor number is the GCF number.
So the greatest common factor 2609,1138 is 1.

Lets's calculate LCM of 688,408

Lowest Common Multiple of 688,408 using Common Division

2	688, 408
2	344, 204
2	172, 102
	86, 51

∴ So the LCM of the given numbers is 2 x 2 x 2 x 86 x 51 = 35088

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/35088

Therefore, the GCF of Fractions 2609/688,1138/408 is 1/35088

Least Common Multiple of 688,408 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 688,408 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(688,408) = 8

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

GCF(688,408) x common factors =8 x 1 = 8

LCM(688,408) = ( 688 × 408 ) / 8

LCM(688,408) = 280704 / 8

LCM(688,408) = 35088

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 2609/688, 1138/408

1. What is the HCF of 2609,1138?

The HCF of 2609,1138 is 1

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 2609/688, 1138/408?

Answer: GCF of Numerators as per given numbers 2609/688, 1138/408 is

GCF of Numerators i.e. for 2609,1138 is 1

LCM of denominators i.e. for 688,408 is 35088.

Thus, GCF of Fractions is 1/35088.Finally, GCF of Fractions for 2609/688, 1138/408 is 1/35088.