How to Find GCF of 384/614, 2072/7852?

GCF of 384/614, 2072/7852

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 384/614, 2072/7852 i.e 8/2410564 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/614, 2072/7852.

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 384/614,2072/7852?

Given fractions are 384/614,2072/7852

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 384/614,2072/7852, numerators are 384,2072

Denominators are 614,7852

The GCF of 384,2072 is 8 .

LCM of 614,7852 is 2410564.

The greatest common factor of 384/614,2072/7852 = [GCF of 384,2072]/[LCM of 614,7852]= 8/2410564

Therefore, the GCF of 384/614,2072/7852 is 8/2410564.

Greatest Common Factor of 384,2072

To find the highest common factor of 384,2072, we have to find the factors of both numbers and list the highest common factor.

The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384

The factors of 2072 are 1, 2, 4, 7, 8, 14, 28, 37, 56, 74, 148, 259, 296, 518, 1036, 2072

The HCF of 384,2072 is 8.

Lets's calculate GCF of 384,2072

Greatest Common Factor (GCF) of 384,2072 By Common Division

2	384, 2072
2	192, 1036
2	96, 518
	48, 259

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 384,2072 By Matching Biggest Common Factor Method

Now, list down the factors of 384

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384

Now, list down the factors of 2072

1,2,4,7,8,14,28,37,56,74,148,259,296,518,1036,2072

Greatest Common Factor

We found the factors 384,2072 . The biggest common factor number is the GCF number.
So the greatest common factor 384,2072 is 8.

Lets's calculate LCM of 614,7852

Lowest Common Multiple of 614,7852 using Common Division

2	614, 7852
	307, 3926

∴ So the LCM of the given numbers is 2 x 307 x 3926 = 2410564

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/2410564

Therefore, the GCF of Fractions 384/614,2072/7852 is 8/2410564

Least Common Multiple of 614,7852 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 614,7852 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(614,7852) = 2

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

GCF(614,7852) x common factors =2 x 1 = 2

LCM(614,7852) = ( 614 × 7852 ) / 2

LCM(614,7852) = 4821128 / 2

LCM(614,7852) = 2410564

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FAQs on GCF of Fractions of 384/614, 2072/7852

1. What is the HCF of 384,2072?

The HCF of 384,2072 is 8

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 384/614, 2072/7852?

Answer: GCF of Numerators as per given numbers 384/614, 2072/7852 is

GCF of Numerators i.e. for 384,2072 is 8

LCM of denominators i.e. for 614,7852 is 2410564.

Thus, GCF of Fractions is 8/2410564.Finally, GCF of Fractions for 384/614, 2072/7852 is 8/2410564.