How to Find GCF of 1690/323, 5102/1591?

GCF of 1690/323, 5102/1591

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 1690/323, 5102/1591 i.e 2/513893 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1690/323, 5102/1591.

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 1690/323,5102/1591?

Given fractions are 1690/323,5102/1591

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 1690/323,5102/1591, numerators are 1690,5102

Denominators are 323,1591

The GCF of 1690,5102 is 2 .

LCM of 323,1591 is 513893.

The greatest common factor of 1690/323,5102/1591 = [GCF of 1690,5102]/[LCM of 323,1591]= 2/513893

Therefore, the GCF of 1690/323,5102/1591 is 2/513893.

Greatest Common Factor of 1690,5102

To find the highest common factor of 1690,5102, we have to find the factors of both numbers and list the highest common factor.

The factors of 1690 are 1, 2, 5, 10, 13, 26, 65, 130, 169, 338, 845, 1690

The factors of 5102 are 1, 2, 2551, 5102

The HCF of 1690,5102 is 2.

Lets's calculate GCF of 1690,5102

Greatest Common Factor (GCF) of 1690,5102 By Common Division

2	1690, 5102
	845, 2551

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

Greatest Common Factor of 1690,5102 By Matching Biggest Common Factor Method

Now, list down the factors of 1690

1,2,5,10,13,26,65,130,169,338,845,1690

Now, list down the factors of 5102

1,2,2551,5102

Greatest Common Factor

We found the factors 1690,5102 . The biggest common factor number is the GCF number.
So the greatest common factor 1690,5102 is 2.

Lets's calculate LCM of 323,1591

Lowest Common Multiple of 323,1591 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 513893

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/513893

Therefore, the GCF of Fractions 1690/323,5102/1591 is 2/513893

Least Common Multiple of 323,1591 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 323,1591 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(323,1591) = 1

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

GCF(323,1591) x common factors =1 x 1 = 1

LCM(323,1591) = ( 323 × 1591 ) / 1

LCM(323,1591) = 513893 / 1

LCM(323,1591) = 513893

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FAQs on GCF of Fractions of 1690/323, 5102/1591

1. What is the HCF of 1690,5102?

The HCF of 1690,5102 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 1690/323, 5102/1591?

Answer: GCF of Numerators as per given numbers 1690/323, 5102/1591 is

GCF of Numerators i.e. for 1690,5102 is 2

LCM of denominators i.e. for 323,1591 is 513893.

Thus, GCF of Fractions is 2/513893.Finally, GCF of Fractions for 1690/323, 5102/1591 is 2/513893.