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GCF of 323/104, 210/364

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 323/104, 210/364 i.e 1/728 easily. The following is the detailed procedure to determine the greatest common factor of fractions 323/104, 210/364.

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 323/104,210/364?

Given fractions are 323/104,210/364

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 323/104,210/364, numerators are 323,210

Denominators are 104,364

The GCF of 323,210 is 1 .

LCM of 104,364 is 728.

The greatest common factor of 323/104,210/364 = [GCF of 323,210]/[LCM of 104,364]= 1/728

Therefore, the GCF of 323/104,210/364 is 1/728.

Greatest Common Factor of 323,210

To find the highest common factor of 323,210, we have to find the factors of both numbers and list the highest common factor.

The factors of 323 are 1, 17, 19, 323

The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

The HCF of 323,210 is 1.

Lets's calculate GCF of 323,210

Greatest Common Factor (GCF) of 323,210 By Common Division

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

Greatest Common Factor of 323,210 By Matching Biggest Common Factor Method

Greatest Common Factor of 323,210 By Matching Biggest Common Factor Method

Now, list down the factors of 323

:

1,17,19,323

Now, list down the factors of 210

:

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Greatest Common Factor

We found the factors 323,210 . The biggest common factor number is the GCF number.
So the greatest common factor 323,210 is 1.

Lets's calculate LCM of 104,364

Lowest Common Multiple of 104,364 using Common Division

2 104, 364
2 52, 182
13 26, 91
2, 7

∴ So the LCM of the given numbers is 2 x 2 x 13 x 2 x 7 = 728

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/728

Therefore, the GCF of Fractions 323/104,210/364 is 1/728

Least Common Multiple of 104,364 with GCF Formula

Least Common Multiple of 104,364 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 104,364 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(104,364) = 52

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

GCF(104,364) x common factors =52 x 1 = 52

LCM(104,364) = ( 104 × 364 ) / 52

LCM(104,364) = 37856 / 52

LCM(104,364) = 728


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FAQs on GCF of Fractions of 323/104, 210/364

1. What is the HCF of 323,210?

The HCF of 323,210 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 323/104, 210/364?

Answer: GCF of Numerators as per given numbers 323/104, 210/364 is

GCF of Numerators i.e. for 323,210 is 1

LCM of denominators i.e. for 104,364 is 728.

Thus, GCF of Fractions is 1/728.Finally, GCF of Fractions for 323/104, 210/364 is 1/728.