How to Find GCF of 594/182, 3969/308?

GCF of 594/182, 3969/308

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 594/182, 3969/308 i.e 27/4004 easily. The following is the detailed procedure to determine the greatest common factor of fractions 594/182, 3969/308.

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 594/182,3969/308?

Given fractions are 594/182,3969/308

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 594/182,3969/308, numerators are 594,3969

Denominators are 182,308

The GCF of 594,3969 is 27 .

LCM of 182,308 is 4004.

The greatest common factor of 594/182,3969/308 = [GCF of 594,3969]/[LCM of 182,308]= 27/4004

Therefore, the GCF of 594/182,3969/308 is 27/4004.

Greatest Common Factor of 594,3969

To find the highest common factor of 594,3969, we have to find the factors of both numbers and list the highest common factor.

The factors of 594 are 1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 99, 198, 297, 594

The factors of 3969 are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 441, 567, 1323, 3969

The HCF of 594,3969 is 27.

Lets's calculate GCF of 594,3969

Greatest Common Factor (GCF) of 594,3969 By Common Division

3	594, 3969
3	198, 1323
3	66, 441
	22, 147

∴ So the GCF of the given numbers is 3 x 3 x 3 = 27

Greatest Common Factor of 594,3969 By Matching Biggest Common Factor Method

Now, list down the factors of 594

1,2,3,6,9,11,18,22,27,33,54,66,99,198,297,594

Now, list down the factors of 3969

1,3,7,9,21,27,49,63,81,147,189,441,567,1323,3969

Greatest Common Factor

We found the factors 594,3969 . The biggest common factor number is the GCF number.
So the greatest common factor 594,3969 is 27.

Lets's calculate LCM of 182,308

Lowest Common Multiple of 182,308 using Common Division

2	182, 308
7	91, 154
	13, 22

∴ So the LCM of the given numbers is 2 x 7 x 13 x 22 = 4004

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/4004

Therefore, the GCF of Fractions 594/182,3969/308 is 27/4004

Least Common Multiple of 182,308 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 182,308 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(182,308) = 14

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

GCF(182,308) x common factors =14 x 1 = 14

LCM(182,308) = ( 182 × 308 ) / 14

LCM(182,308) = 56056 / 14

LCM(182,308) = 4004

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FAQs on GCF of Fractions of 594/182, 3969/308

1. What is the HCF of 594,3969?

The HCF of 594,3969 is 27

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 594/182, 3969/308?

Answer: GCF of Numerators as per given numbers 594/182, 3969/308 is

GCF of Numerators i.e. for 594,3969 is 27

LCM of denominators i.e. for 182,308 is 4004.

Thus, GCF of Fractions is 27/4004.Finally, GCF of Fractions for 594/182, 3969/308 is 27/4004.