How to Find GCF of 578/91, 714/872?

GCF of 578/91, 714/872

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 578/91, 714/872 i.e 34/79352 easily. The following is the detailed procedure to determine the greatest common factor of fractions 578/91, 714/872.

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 578/91,714/872?

Given fractions are 578/91,714/872

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 578/91,714/872, numerators are 578,714

Denominators are 91,872

The GCF of 578,714 is 34 .

LCM of 91,872 is 79352.

The greatest common factor of 578/91,714/872 = [GCF of 578,714]/[LCM of 91,872]= 34/79352

Therefore, the GCF of 578/91,714/872 is 34/79352.

Greatest Common Factor of 578,714

To find the highest common factor of 578,714, we have to find the factors of both numbers and list the highest common factor.

The factors of 578 are 1, 2, 17, 34, 289, 578

The factors of 714 are 1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714

The HCF of 578,714 is 34.

Lets's calculate GCF of 578,714

Greatest Common Factor (GCF) of 578,714 By Common Division

2	578, 714
17	289, 357
	17, 21

∴ So the GCF of the given numbers is 2 x 17 = 34

Greatest Common Factor of 578,714 By Matching Biggest Common Factor Method

Now, list down the factors of 578

1,2,17,34,289,578

Now, list down the factors of 714

1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714

Greatest Common Factor

We found the factors 578,714 . The biggest common factor number is the GCF number.
So the greatest common factor 578,714 is 34.

Lets's calculate LCM of 91,872

Lowest Common Multiple of 91,872 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 79352

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/79352

Therefore, the GCF of Fractions 578/91,714/872 is 34/79352

Least Common Multiple of 91,872 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 91,872 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(91,872) = 1

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

GCF(91,872) x common factors =1 x 1 = 1

LCM(91,872) = ( 91 × 872 ) / 1

LCM(91,872) = 79352 / 1

LCM(91,872) = 79352

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FAQs on GCF of Fractions of 578/91, 714/872

1. What is the HCF of 578,714?

The HCF of 578,714 is 34

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 578/91, 714/872?

Answer: GCF of Numerators as per given numbers 578/91, 714/872 is

GCF of Numerators i.e. for 578,714 is 34

LCM of denominators i.e. for 91,872 is 79352.

Thus, GCF of Fractions is 34/79352.Finally, GCF of Fractions for 578/91, 714/872 is 34/79352.