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GCF of 349/31, 382/194

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 349/31, 382/194 i.e 1/6014 easily. The following is the detailed procedure to determine the greatest common factor of fractions 349/31, 382/194.

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 349/31,382/194?

Given fractions are 349/31,382/194

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 349/31,382/194, numerators are 349,382

Denominators are 31,194

The GCF of 349,382 is 1 .

LCM of 31,194 is 6014.

The greatest common factor of 349/31,382/194 = [GCF of 349,382]/[LCM of 31,194]= 1/6014

Therefore, the GCF of 349/31,382/194 is 1/6014.

Greatest Common Factor of 349,382

To find the highest common factor of 349,382, we have to find the factors of both numbers and list the highest common factor.

The factors of 349 are 1, 349

The factors of 382 are 1, 2, 191, 382

The HCF of 349,382 is 1.

Lets's calculate GCF of 349,382

Greatest Common Factor (GCF) of 349,382 By Common Division

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

Greatest Common Factor of 349,382 By Matching Biggest Common Factor Method

Greatest Common Factor of 349,382 By Matching Biggest Common Factor Method

Now, list down the factors of 349

:

1,349

Now, list down the factors of 382

:

1,2,191,382

Greatest Common Factor

We found the factors 349,382 . The biggest common factor number is the GCF number.
So the greatest common factor 349,382 is 1.

Lets's calculate LCM of 31,194

Lowest Common Multiple of 31,194 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 6014

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6014

Therefore, the GCF of Fractions 349/31,382/194 is 1/6014

Least Common Multiple of 31,194 with GCF Formula

Least Common Multiple of 31,194 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 31,194 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,194) = 1

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

GCF(31,194) x common factors =1 x 1 = 1

LCM(31,194) = ( 31 × 194 ) / 1

LCM(31,194) = 6014 / 1

LCM(31,194) = 6014


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FAQs on GCF of Fractions of 349/31, 382/194

1. What is the HCF of 349,382?

The HCF of 349,382 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 349/31, 382/194?

Answer: GCF of Numerators as per given numbers 349/31, 382/194 is

GCF of Numerators i.e. for 349,382 is 1

LCM of denominators i.e. for 31,194 is 6014.

Thus, GCF of Fractions is 1/6014.Finally, GCF of Fractions for 349/31, 382/194 is 1/6014.