How to Find GCF of 54/43, 199/45, 688/854?

GCF of 54/43, 199/45, 688/854

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 54/43, 199/45, 688/854 i.e 1/1652490 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/43, 199/45, 688/854.

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 54/43,199/45,688/854?

Given fractions are 54/43,199/45,688/854

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 54/43,199/45,688/854, numerators are 54,199,688

Denominators are 43,45,854

The GCF of 54,199,688 is 1 .

LCM of 43,45,854 is 1652490.

The greatest common factor of 54/43,199/45,688/854 = [GCF of 54,199,688]/[LCM of 43,45,854]= 1/1652490

Therefore, the GCF of 54/43,199/45,688/854 is 1/1652490.

Greatest Common Factor of 54,199,688

To find the highest common factor of 54,199,688, we have to find the factors of both numbers and list the highest common factor.

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54

The factors of 199 are 1, 199

The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688

The HCF of 54,199,688 is 1.

Lets's calculate GCF of 54,199,688

Greatest Common Factor (GCF) of 54,199,688 By Common Division

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

Greatest Common Factor of 54,199,688 By Matching Biggest Common Factor Method

Now, list down the factors of 54

1,2,3,6,9,18,27,54

Now, list down the factors of 199

1,199

Now, list down the factors of 688

1,2,4,8,16,43,86,172,344,688

Greatest Common Factor

We found the factors 54,199,688 . The biggest common factor number is the GCF number.
So the greatest common factor 54,199,688 is 1.

Lets's calculate LCM of 43,45,854

Lowest Common Multiple of 43,45,854 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1652490

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1652490

Therefore, the GCF of Fractions 54/43,199/45,688/854 is 1/1652490

Least Common Multiple of 43,45,854 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 43,45,854 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(43,45,854) = 1

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

GCF(43,45,854) x common factors =1 x 1 = 1

LCM(43,45,854) = ( 43 × 45 × 854 ) / 1

LCM(43,45,854) = 1652490 / 1

LCM(43,45,854) = 1652490

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FAQs on GCF of Fractions of 54/43, 199/45, 688/854

1. What is the HCF of 54,199,688?

The HCF of 54,199,688 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 54/43, 199/45, 688/854?

Answer: GCF of Numerators as per given numbers 54/43, 199/45, 688/854 is

GCF of Numerators i.e. for 54,199,688 is 1

LCM of denominators i.e. for 43,45,854 is 1652490.

Thus, GCF of Fractions is 1/1652490.Finally, GCF of Fractions for 54/43, 199/45, 688/854 is 1/1652490.