How to Find GCF of 59/123, 80/214, 354/554?

GCF of 59/123, 80/214, 354/554

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 59/123, 80/214, 354/554 i.e 1/7291194 easily. The following is the detailed procedure to determine the greatest common factor of fractions 59/123, 80/214, 354/554.

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 59/123,80/214,354/554?

Given fractions are 59/123,80/214,354/554

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 59/123,80/214,354/554, numerators are 59,80,354

Denominators are 123,214,554

The GCF of 59,80,354 is 1 .

LCM of 123,214,554 is 7291194.

The greatest common factor of 59/123,80/214,354/554 = [GCF of 59,80,354]/[LCM of 123,214,554]= 1/7291194

Therefore, the GCF of 59/123,80/214,354/554 is 1/7291194.

Greatest Common Factor of 59,80,354

To find the highest common factor of 59,80,354, we have to find the factors of both numbers and list the highest common factor.

The factors of 59 are 1, 59

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

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

The HCF of 59,80,354 is 1.

Lets's calculate GCF of 59,80,354

Greatest Common Factor (GCF) of 59,80,354 By Common Division

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

Greatest Common Factor of 59,80,354 By Matching Biggest Common Factor Method

Now, list down the factors of 59

1,59

Now, list down the factors of 80

1,2,4,5,8,10,16,20,40,80

Now, list down the factors of 354

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

Greatest Common Factor

We found the factors 59,80,354 . The biggest common factor number is the GCF number.
So the greatest common factor 59,80,354 is 1.

Lets's calculate LCM of 123,214,554

Lowest Common Multiple of 123,214,554 using Common Division

2	123, 214, 554
	123, 107, 277

∴ So the LCM of the given numbers is 2 x 123 x 107 x 277 = 7291194

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7291194

Therefore, the GCF of Fractions 59/123,80/214,354/554 is 1/7291194

Least Common Multiple of 123,214,554 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 123,214,554 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(123,214,554) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(123,214,554) x common factors =1 x 2 = 2

LCM(123,214,554) = ( 123 × 214 × 554 ) / 2

LCM(123,214,554) = 14582388 / 2

LCM(123,214,554) = 7291194

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 59/123, 80/214, 354/554

1. What is the HCF of 59,80,354?

The HCF of 59,80,354 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 59/123, 80/214, 354/554?

Answer: GCF of Numerators as per given numbers 59/123, 80/214, 354/554 is

GCF of Numerators i.e. for 59,80,354 is 1

LCM of denominators i.e. for 123,214,554 is 7291194.

Thus, GCF of Fractions is 1/7291194.Finally, GCF of Fractions for 59/123, 80/214, 354/554 is 1/7291194.