How to Find GCF of 1744/489, 5072/8054?

GCF of 1744/489, 5072/8054

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 1744/489, 5072/8054 i.e 16/3938406 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1744/489, 5072/8054.

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 1744/489,5072/8054?

Given fractions are 1744/489,5072/8054

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 1744/489,5072/8054, numerators are 1744,5072

Denominators are 489,8054

The GCF of 1744,5072 is 16 .

LCM of 489,8054 is 3938406.

The greatest common factor of 1744/489,5072/8054 = [GCF of 1744,5072]/[LCM of 489,8054]= 16/3938406

Therefore, the GCF of 1744/489,5072/8054 is 16/3938406.

Greatest Common Factor of 1744,5072

To find the highest common factor of 1744,5072, we have to find the factors of both numbers and list the highest common factor.

The factors of 1744 are 1, 2, 4, 8, 16, 109, 218, 436, 872, 1744

The factors of 5072 are 1, 2, 4, 8, 16, 317, 634, 1268, 2536, 5072

The HCF of 1744,5072 is 16.

Lets's calculate GCF of 1744,5072

Greatest Common Factor (GCF) of 1744,5072 By Common Division

2	1744, 5072
2	872, 2536
2	436, 1268
2	218, 634
	109, 317

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 1744,5072 By Matching Biggest Common Factor Method

Now, list down the factors of 1744

1,2,4,8,16,109,218,436,872,1744

Now, list down the factors of 5072

1,2,4,8,16,317,634,1268,2536,5072

Greatest Common Factor

We found the factors 1744,5072 . The biggest common factor number is the GCF number.
So the greatest common factor 1744,5072 is 16.

Lets's calculate LCM of 489,8054

Lowest Common Multiple of 489,8054 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3938406

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/3938406

Therefore, the GCF of Fractions 1744/489,5072/8054 is 16/3938406

Least Common Multiple of 489,8054 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 489,8054 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(489,8054) = 1

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

GCF(489,8054) x common factors =1 x 1 = 1

LCM(489,8054) = ( 489 × 8054 ) / 1

LCM(489,8054) = 3938406 / 1

LCM(489,8054) = 3938406

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FAQs on GCF of Fractions of 1744/489, 5072/8054

1. What is the HCF of 1744,5072?

The HCF of 1744,5072 is 16

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 1744/489, 5072/8054?

Answer: GCF of Numerators as per given numbers 1744/489, 5072/8054 is

GCF of Numerators i.e. for 1744,5072 is 16

LCM of denominators i.e. for 489,8054 is 3938406.

Thus, GCF of Fractions is 16/3938406.Finally, GCF of Fractions for 1744/489, 5072/8054 is 16/3938406.