How to Find GCF of 354/31, 657/85, 466/73?

GCF of 354/31, 657/85, 466/73

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 354/31, 657/85, 466/73 i.e 1/192355 easily. The following is the detailed procedure to determine the greatest common factor of fractions 354/31, 657/85, 466/73.

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 354/31,657/85,466/73?

Given fractions are 354/31,657/85,466/73

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 354/31,657/85,466/73, numerators are 354,657,466

Denominators are 31,85,73

The GCF of 354,657,466 is 1 .

LCM of 31,85,73 is 192355.

The greatest common factor of 354/31,657/85,466/73 = [GCF of 354,657,466]/[LCM of 31,85,73]= 1/192355

Therefore, the GCF of 354/31,657/85,466/73 is 1/192355.

Greatest Common Factor of 354,657,466

To find the highest common factor of 354,657,466, we have to find the factors of both numbers and list the highest common factor.

The factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354

The factors of 657 are 1, 3, 9, 73, 219, 657

The factors of 466 are 1, 2, 233, 466

The HCF of 354,657,466 is 1.

Lets's calculate GCF of 354,657,466

Greatest Common Factor (GCF) of 354,657,466 By Common Division

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

Greatest Common Factor of 354,657,466 By Matching Biggest Common Factor Method

Now, list down the factors of 354

1,2,3,6,59,118,177,354

Now, list down the factors of 657

1,3,9,73,219,657

Now, list down the factors of 466

1,2,233,466

Greatest Common Factor

We found the factors 354,657,466 . The biggest common factor number is the GCF number.
So the greatest common factor 354,657,466 is 1.

Lets's calculate LCM of 31,85,73

Lowest Common Multiple of 31,85,73 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 192355

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/192355

Therefore, the GCF of Fractions 354/31,657/85,466/73 is 1/192355

Least Common Multiple of 31,85,73 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 31,85,73 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,85,73) = 1

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

GCF(31,85,73) x common factors =1 x 1 = 1

LCM(31,85,73) = ( 31 × 85 × 73 ) / 1

LCM(31,85,73) = 192355 / 1

LCM(31,85,73) = 192355

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FAQs on GCF of Fractions of 354/31, 657/85, 466/73

1. What is the HCF of 354,657,466?

The HCF of 354,657,466 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 354/31, 657/85, 466/73?

Answer: GCF of Numerators as per given numbers 354/31, 657/85, 466/73 is

GCF of Numerators i.e. for 354,657,466 is 1

LCM of denominators i.e. for 31,85,73 is 192355.

Thus, GCF of Fractions is 1/192355.Finally, GCF of Fractions for 354/31, 657/85, 466/73 is 1/192355.