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GCF of 749/54, 108/194

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 749/54, 108/194 i.e 1/5238 easily. The following is the detailed procedure to determine the greatest common factor of fractions 749/54, 108/194.

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 749/54,108/194?

Given fractions are 749/54,108/194

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 749/54,108/194, numerators are 749,108

Denominators are 54,194

The GCF of 749,108 is 1 .

LCM of 54,194 is 5238.

The greatest common factor of 749/54,108/194 = [GCF of 749,108]/[LCM of 54,194]= 1/5238

Therefore, the GCF of 749/54,108/194 is 1/5238.

Greatest Common Factor of 749,108

To find the highest common factor of 749,108, we have to find the factors of both numbers and list the highest common factor.

The factors of 749 are 1, 7, 107, 749

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

The HCF of 749,108 is 1.

Lets's calculate GCF of 749,108

Greatest Common Factor (GCF) of 749,108 By Common Division

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

Greatest Common Factor of 749,108 By Matching Biggest Common Factor Method

Greatest Common Factor of 749,108 By Matching Biggest Common Factor Method

Now, list down the factors of 749

:

1,7,107,749

Now, list down the factors of 108

:

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

Greatest Common Factor

We found the factors 749,108 . The biggest common factor number is the GCF number.
So the greatest common factor 749,108 is 1.

Lets's calculate LCM of 54,194

Lowest Common Multiple of 54,194 using Common Division

2 54, 194
27, 97

∴ So the LCM of the given numbers is 2 x 27 x 97 = 5238

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5238

Therefore, the GCF of Fractions 749/54,108/194 is 1/5238

Least Common Multiple of 54,194 with GCF Formula

Least Common Multiple of 54,194 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 54,194 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(54,194) = 2

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

GCF(54,194) x common factors =2 x 1 = 2

LCM(54,194) = ( 54 × 194 ) / 2

LCM(54,194) = 10476 / 2

LCM(54,194) = 5238


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FAQs on GCF of Fractions of 749/54, 108/194

1. What is the HCF of 749,108?

The HCF of 749,108 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 749/54, 108/194?

Answer: GCF of Numerators as per given numbers 749/54, 108/194 is

GCF of Numerators i.e. for 749,108 is 1

LCM of denominators i.e. for 54,194 is 5238.

Thus, GCF of Fractions is 1/5238.Finally, GCF of Fractions for 749/54, 108/194 is 1/5238.