How to Find GCF of 581/684, 978/456?

GCF of 581/684, 978/456

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 581/684, 978/456 i.e 1/1368 easily. The following is the detailed procedure to determine the greatest common factor of fractions 581/684, 978/456.

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 581/684,978/456?

Given fractions are 581/684,978/456

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 581/684,978/456, numerators are 581,978

Denominators are 684,456

The GCF of 581,978 is 1 .

LCM of 684,456 is 1368.

The greatest common factor of 581/684,978/456 = [GCF of 581,978]/[LCM of 684,456]= 1/1368

Therefore, the GCF of 581/684,978/456 is 1/1368.

Greatest Common Factor of 581,978

To find the highest common factor of 581,978, we have to find the factors of both numbers and list the highest common factor.

The factors of 581 are 1, 7, 83, 581

The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978

The HCF of 581,978 is 1.

Lets's calculate GCF of 581,978

Greatest Common Factor (GCF) of 581,978 By Common Division

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

Greatest Common Factor of 581,978 By Matching Biggest Common Factor Method

Now, list down the factors of 581

1,7,83,581

Now, list down the factors of 978

1,2,3,6,163,326,489,978

Greatest Common Factor

We found the factors 581,978 . The biggest common factor number is the GCF number.
So the greatest common factor 581,978 is 1.

Lets's calculate LCM of 684,456

Lowest Common Multiple of 684,456 using Common Division

2	684, 456
2	342, 228
3	171, 114
19	57, 38
	3, 2

∴ So the LCM of the given numbers is 2 x 2 x 3 x 19 x 3 x 2 = 1368

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1368

Therefore, the GCF of Fractions 581/684,978/456 is 1/1368

Least Common Multiple of 684,456 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 684,456 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(684,456) = 228

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

GCF(684,456) x common factors =228 x 1 = 228

LCM(684,456) = ( 684 × 456 ) / 228

LCM(684,456) = 311904 / 228

LCM(684,456) = 1368

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FAQs on GCF of Fractions of 581/684, 978/456

1. What is the HCF of 581,978?

The HCF of 581,978 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 581/684, 978/456?

Answer: GCF of Numerators as per given numbers 581/684, 978/456 is

GCF of Numerators i.e. for 581,978 is 1

LCM of denominators i.e. for 684,456 is 1368.

Thus, GCF of Fractions is 1/1368.Finally, GCF of Fractions for 581/684, 978/456 is 1/1368.