How to Find GCF of 4134/269, 1999/7972?

GCF of 4134/269, 1999/7972

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 4134/269, 1999/7972 i.e 1/2144468 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4134/269, 1999/7972.

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 4134/269,1999/7972?

Given fractions are 4134/269,1999/7972

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 4134/269,1999/7972, numerators are 4134,1999

Denominators are 269,7972

The GCF of 4134,1999 is 1 .

LCM of 269,7972 is 2144468.

The greatest common factor of 4134/269,1999/7972 = [GCF of 4134,1999]/[LCM of 269,7972]= 1/2144468

Therefore, the GCF of 4134/269,1999/7972 is 1/2144468.

Greatest Common Factor of 4134,1999

To find the highest common factor of 4134,1999, we have to find the factors of both numbers and list the highest common factor.

The factors of 4134 are 1, 2, 3, 6, 13, 26, 39, 53, 78, 106, 159, 318, 689, 1378, 2067, 4134

The factors of 1999 are 1, 1999

The HCF of 4134,1999 is 1.

Lets's calculate GCF of 4134,1999

Greatest Common Factor (GCF) of 4134,1999 By Common Division

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

Greatest Common Factor of 4134,1999 By Matching Biggest Common Factor Method

Now, list down the factors of 4134

1,2,3,6,13,26,39,53,78,106,159,318,689,1378,2067,4134

Now, list down the factors of 1999

1,1999

Greatest Common Factor

We found the factors 4134,1999 . The biggest common factor number is the GCF number.
So the greatest common factor 4134,1999 is 1.

Lets's calculate LCM of 269,7972

Lowest Common Multiple of 269,7972 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2144468

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2144468

Therefore, the GCF of Fractions 4134/269,1999/7972 is 1/2144468

Least Common Multiple of 269,7972 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 269,7972 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(269,7972) = 1

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

GCF(269,7972) x common factors =1 x 1 = 1

LCM(269,7972) = ( 269 × 7972 ) / 1

LCM(269,7972) = 2144468 / 1

LCM(269,7972) = 2144468

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FAQs on GCF of Fractions of 4134/269, 1999/7972

1. What is the HCF of 4134,1999?

The HCF of 4134,1999 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 4134/269, 1999/7972?

Answer: GCF of Numerators as per given numbers 4134/269, 1999/7972 is

GCF of Numerators i.e. for 4134,1999 is 1

LCM of denominators i.e. for 269,7972 is 2144468.

Thus, GCF of Fractions is 1/2144468.Finally, GCF of Fractions for 4134/269, 1999/7972 is 1/2144468.