How to Find GCF of 4122/408, 3155/7872?

GCF of 4122/408, 3155/7872

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 4122/408, 3155/7872 i.e 1/133824 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4122/408, 3155/7872.

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 4122/408,3155/7872?

Given fractions are 4122/408,3155/7872

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 4122/408,3155/7872, numerators are 4122,3155

Denominators are 408,7872

The GCF of 4122,3155 is 1 .

LCM of 408,7872 is 133824.

The greatest common factor of 4122/408,3155/7872 = [GCF of 4122,3155]/[LCM of 408,7872]= 1/133824

Therefore, the GCF of 4122/408,3155/7872 is 1/133824.

Greatest Common Factor of 4122,3155

To find the highest common factor of 4122,3155, we have to find the factors of both numbers and list the highest common factor.

The factors of 4122 are 1, 2, 3, 6, 9, 18, 229, 458, 687, 1374, 2061, 4122

The factors of 3155 are 1, 5, 631, 3155

The HCF of 4122,3155 is 1.

Lets's calculate GCF of 4122,3155

Greatest Common Factor (GCF) of 4122,3155 By Common Division

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

Greatest Common Factor of 4122,3155 By Matching Biggest Common Factor Method

Now, list down the factors of 4122

1,2,3,6,9,18,229,458,687,1374,2061,4122

Now, list down the factors of 3155

1,5,631,3155

Greatest Common Factor

We found the factors 4122,3155 . The biggest common factor number is the GCF number.
So the greatest common factor 4122,3155 is 1.

Lets's calculate LCM of 408,7872

Lowest Common Multiple of 408,7872 using Common Division

2	408, 7872
2	204, 3936
2	102, 1968
3	51, 984
	17, 328

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 17 x 328 = 133824

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/133824

Therefore, the GCF of Fractions 4122/408,3155/7872 is 1/133824

Least Common Multiple of 408,7872 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 408,7872 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(408,7872) = 24

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

GCF(408,7872) x common factors =24 x 1 = 24

LCM(408,7872) = ( 408 × 7872 ) / 24

LCM(408,7872) = 3211776 / 24

LCM(408,7872) = 133824

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FAQs on GCF of Fractions of 4122/408, 3155/7872

1. What is the HCF of 4122,3155?

The HCF of 4122,3155 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 4122/408, 3155/7872?

Answer: GCF of Numerators as per given numbers 4122/408, 3155/7872 is

GCF of Numerators i.e. for 4122,3155 is 1

LCM of denominators i.e. for 408,7872 is 133824.

Thus, GCF of Fractions is 1/133824.Finally, GCF of Fractions for 4122/408, 3155/7872 is 1/133824.