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GCF of 209/838, 9105/172

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 209/838, 9105/172 i.e 1/72068 easily. The following is the detailed procedure to determine the greatest common factor of fractions 209/838, 9105/172.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 209/838,9105/172?

Given fractions are 209/838,9105/172

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 209/838,9105/172, numerators are 209,9105

Denominators are 838,172

The GCF of 209,9105 is 1 .

LCM of 838,172 is 72068.

The greatest common factor of 209/838,9105/172 = [GCF of 209,9105]/[LCM of 838,172]= 1/72068

Therefore, the GCF of 209/838,9105/172 is 1/72068.

Greatest Common Factor of 209,9105

To find the highest common factor of 209,9105, we have to find the factors of both numbers and list the highest common factor.

The factors of 209 are 1, 11, 19, 209

The factors of 9105 are 1, 3, 5, 15, 607, 1821, 3035, 9105

The HCF of 209,9105 is 1.

Lets's calculate GCF of 209,9105

Greatest Common Factor (GCF) of 209,9105 By Common Division

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

Greatest Common Factor of 209,9105 By Matching Biggest Common Factor Method

Greatest Common Factor of 209,9105 By Matching Biggest Common Factor Method

Now, list down the factors of 209

:

1,11,19,209

Now, list down the factors of 9105

:

1,3,5,15,607,1821,3035,9105

Greatest Common Factor

We found the factors 209,9105 . The biggest common factor number is the GCF number.
So the greatest common factor 209,9105 is 1.

Lets's calculate LCM of 838,172

Lowest Common Multiple of 838,172 using Common Division

2 838, 172
419, 86

∴ So the LCM of the given numbers is 2 x 419 x 86 = 72068

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/72068

Therefore, the GCF of Fractions 209/838,9105/172 is 1/72068

Least Common Multiple of 838,172 with GCF Formula

Least Common Multiple of 838,172 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 838,172 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(838,172) = 2

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

GCF(838,172) x common factors =2 x 1 = 2

LCM(838,172) = ( 838 × 172 ) / 2

LCM(838,172) = 144136 / 2

LCM(838,172) = 72068


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FAQs on GCF of Fractions of 209/838, 9105/172

1. What is the HCF of 209,9105?

The HCF of 209,9105 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 209/838, 9105/172?

Answer: GCF of Numerators as per given numbers 209/838, 9105/172 is

GCF of Numerators i.e. for 209,9105 is 1

LCM of denominators i.e. for 838,172 is 72068.

Thus, GCF of Fractions is 1/72068.Finally, GCF of Fractions for 209/838, 9105/172 is 1/72068.