How to Find GCF of 43/50, 64/52, 208/29?

GCF of 43/50, 64/52, 208/29

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 43/50, 64/52, 208/29 i.e 1/37700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/50, 64/52, 208/29.

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 43/50,64/52,208/29?

Given fractions are 43/50,64/52,208/29

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 43/50,64/52,208/29, numerators are 43,64,208

Denominators are 50,52,29

The GCF of 43,64,208 is 1 .

LCM of 50,52,29 is 37700.

The greatest common factor of 43/50,64/52,208/29 = [GCF of 43,64,208]/[LCM of 50,52,29]= 1/37700

Therefore, the GCF of 43/50,64/52,208/29 is 1/37700.

Greatest Common Factor of 43,64,208

To find the highest common factor of 43,64,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 43 are 1, 43

The factors of 64 are 1, 2, 4, 8, 16, 32, 64

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 43,64,208 is 1.

Lets's calculate GCF of 43,64,208

Greatest Common Factor (GCF) of 43,64,208 By Common Division

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

Greatest Common Factor of 43,64,208 By Matching Biggest Common Factor Method

Now, list down the factors of 43

1,43

Now, list down the factors of 64

1,2,4,8,16,32,64

Now, list down the factors of 208

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 43,64,208 . The biggest common factor number is the GCF number.
So the greatest common factor 43,64,208 is 1.

Lets's calculate LCM of 50,52,29

Lowest Common Multiple of 50,52,29 using Common Division

2	50, 52, 29
	25, 26, 29

∴ So the LCM of the given numbers is 2 x 25 x 26 x 29 = 37700

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/37700

Therefore, the GCF of Fractions 43/50,64/52,208/29 is 1/37700

Least Common Multiple of 50,52,29 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 50,52,29 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(50,52,29) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(50,52,29) x common factors =1 x 2 = 2

LCM(50,52,29) = ( 50 × 52 × 29 ) / 2

LCM(50,52,29) = 75400 / 2

LCM(50,52,29) = 37700

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FAQs on GCF of Fractions of 43/50, 64/52, 208/29

1. What is the HCF of 43,64,208?

The HCF of 43,64,208 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 43/50, 64/52, 208/29?

Answer: GCF of Numerators as per given numbers 43/50, 64/52, 208/29 is

GCF of Numerators i.e. for 43,64,208 is 1

LCM of denominators i.e. for 50,52,29 is 37700.

Thus, GCF of Fractions is 1/37700.Finally, GCF of Fractions for 43/50, 64/52, 208/29 is 1/37700.