How to Find GCF of 108/209, 402/798?

GCF of 108/209, 402/798

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 108/209, 402/798 i.e 6/8778 easily. The following is the detailed procedure to determine the greatest common factor of fractions 108/209, 402/798.

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 108/209,402/798?

Given fractions are 108/209,402/798

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 108/209,402/798, numerators are 108,402

Denominators are 209,798

The GCF of 108,402 is 6 .

LCM of 209,798 is 8778.

The greatest common factor of 108/209,402/798 = [GCF of 108,402]/[LCM of 209,798]= 6/8778

Therefore, the GCF of 108/209,402/798 is 6/8778.

Greatest Common Factor of 108,402

To find the highest common factor of 108,402, we have to find the factors of both numbers and list the highest common factor.

The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402

The HCF of 108,402 is 6.

Lets's calculate GCF of 108,402

Greatest Common Factor (GCF) of 108,402 By Common Division

2	108, 402
3	54, 201
	18, 67

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

Greatest Common Factor of 108,402 By Matching Biggest Common Factor Method

Now, list down the factors of 108

1,2,3,4,6,9,12,18,27,36,54,108

Now, list down the factors of 402

1,2,3,6,67,134,201,402

Greatest Common Factor

We found the factors 108,402 . The biggest common factor number is the GCF number.
So the greatest common factor 108,402 is 6.

Lets's calculate LCM of 209,798

Lowest Common Multiple of 209,798 using Common Division

19	209, 798
	11, 42

∴ So the LCM of the given numbers is 19 x 11 x 42 = 8778

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/8778

Therefore, the GCF of Fractions 108/209,402/798 is 6/8778

Least Common Multiple of 209,798 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 209,798 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(209,798) = 19

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

GCF(209,798) x common factors =19 x 1 = 19

LCM(209,798) = ( 209 × 798 ) / 19

LCM(209,798) = 166782 / 19

LCM(209,798) = 8778

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FAQs on GCF of Fractions of 108/209, 402/798

1. What is the HCF of 108,402?

The HCF of 108,402 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 108/209, 402/798?

Answer: GCF of Numerators as per given numbers 108/209, 402/798 is

GCF of Numerators i.e. for 108,402 is 6

LCM of denominators i.e. for 209,798 is 8778.

Thus, GCF of Fractions is 6/8778.Finally, GCF of Fractions for 108/209, 402/798 is 6/8778.