How to Find GCF of 4132/408, 4189/5456?

GCF of 4132/408, 4189/5456

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 4132/408, 4189/5456 i.e 1/278256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4132/408, 4189/5456.

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 4132/408,4189/5456?

Given fractions are 4132/408,4189/5456

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 4132/408,4189/5456, numerators are 4132,4189

Denominators are 408,5456

The GCF of 4132,4189 is 1 .

LCM of 408,5456 is 278256.

The greatest common factor of 4132/408,4189/5456 = [GCF of 4132,4189]/[LCM of 408,5456]= 1/278256

Therefore, the GCF of 4132/408,4189/5456 is 1/278256.

Greatest Common Factor of 4132,4189

To find the highest common factor of 4132,4189, we have to find the factors of both numbers and list the highest common factor.

The factors of 4132 are 1, 2, 4, 1033, 2066, 4132

The factors of 4189 are 1, 59, 71, 4189

The HCF of 4132,4189 is 1.

Lets's calculate GCF of 4132,4189

Greatest Common Factor (GCF) of 4132,4189 By Common Division

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

Greatest Common Factor of 4132,4189 By Matching Biggest Common Factor Method

Now, list down the factors of 4132

1,2,4,1033,2066,4132

Now, list down the factors of 4189

1,59,71,4189

Greatest Common Factor

We found the factors 4132,4189 . The biggest common factor number is the GCF number.
So the greatest common factor 4132,4189 is 1.

Lets's calculate LCM of 408,5456

Lowest Common Multiple of 408,5456 using Common Division

2	408, 5456
2	204, 2728
2	102, 1364
	51, 682

∴ So the LCM of the given numbers is 2 x 2 x 2 x 51 x 682 = 278256

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/278256

Therefore, the GCF of Fractions 4132/408,4189/5456 is 1/278256

Least Common Multiple of 408,5456 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 408,5456 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(408,5456) = 8

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

GCF(408,5456) x common factors =8 x 1 = 8

LCM(408,5456) = ( 408 × 5456 ) / 8

LCM(408,5456) = 2226048 / 8

LCM(408,5456) = 278256

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FAQs on GCF of Fractions of 4132/408, 4189/5456

1. What is the HCF of 4132,4189?

The HCF of 4132,4189 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 4132/408, 4189/5456?

Answer: GCF of Numerators as per given numbers 4132/408, 4189/5456 is

GCF of Numerators i.e. for 4132,4189 is 1

LCM of denominators i.e. for 408,5456 is 278256.

Thus, GCF of Fractions is 1/278256.Finally, GCF of Fractions for 4132/408, 4189/5456 is 1/278256.