How to Find GCF of 34/80, 209/60, 181/474?

GCF of 34/80, 209/60, 181/474

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 34/80, 209/60, 181/474 i.e 1/18960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/80, 209/60, 181/474.

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 34/80,209/60,181/474?

Given fractions are 34/80,209/60,181/474

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 34/80,209/60,181/474, numerators are 34,209,181

Denominators are 80,60,474

The GCF of 34,209,181 is 1 .

LCM of 80,60,474 is 18960.

The greatest common factor of 34/80,209/60,181/474 = [GCF of 34,209,181]/[LCM of 80,60,474]= 1/18960

Therefore, the GCF of 34/80,209/60,181/474 is 1/18960.

Greatest Common Factor of 34,209,181

To find the highest common factor of 34,209,181, we have to find the factors of both numbers and list the highest common factor.

The factors of 34 are 1, 2, 17, 34

The factors of 209 are 1, 11, 19, 209

The factors of 181 are 1, 181

The HCF of 34,209,181 is 1.

Lets's calculate GCF of 34,209,181

Greatest Common Factor (GCF) of 34,209,181 By Common Division

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

Greatest Common Factor of 34,209,181 By Matching Biggest Common Factor Method

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 209

1,11,19,209

Now, list down the factors of 181

1,181

Greatest Common Factor

We found the factors 34,209,181 . The biggest common factor number is the GCF number.
So the greatest common factor 34,209,181 is 1.

Lets's calculate LCM of 80,60,474

Lowest Common Multiple of 80,60,474 using Common Division

2	80, 60, 474
2	40, 30, 237
3	20, 15, 237
5	20, 5, 79
	4, 1, 79

∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 4 x 1 x 79 = 18960

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18960

Therefore, the GCF of Fractions 34/80,209/60,181/474 is 1/18960

Least Common Multiple of 80,60,474 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 80,60,474 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(80,60,474) = 2

common factors(in case of two or more numbers have common factors) = 60

GCF(80,60,474) x common factors =2 x 60 = 120

LCM(80,60,474) = ( 80 × 60 × 474 ) / 120

LCM(80,60,474) = 2275200 / 120

LCM(80,60,474) = 18960

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FAQs on GCF of Fractions of 34/80, 209/60, 181/474

1. What is the HCF of 34,209,181?

The HCF of 34,209,181 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 34/80, 209/60, 181/474?

Answer: GCF of Numerators as per given numbers 34/80, 209/60, 181/474 is

GCF of Numerators i.e. for 34,209,181 is 1

LCM of denominators i.e. for 80,60,474 is 18960.

Thus, GCF of Fractions is 1/18960.Finally, GCF of Fractions for 34/80, 209/60, 181/474 is 1/18960.