How to Find GCF of 364/128, 208/846?

GCF of 364/128, 208/846

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 364/128, 208/846 i.e 52/54144 easily. The following is the detailed procedure to determine the greatest common factor of fractions 364/128, 208/846.

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 364/128,208/846?

Given fractions are 364/128,208/846

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 364/128,208/846, numerators are 364,208

Denominators are 128,846

The GCF of 364,208 is 52 .

LCM of 128,846 is 54144.

The greatest common factor of 364/128,208/846 = [GCF of 364,208]/[LCM of 128,846]= 52/54144

Therefore, the GCF of 364/128,208/846 is 52/54144.

Greatest Common Factor of 364,208

To find the highest common factor of 364,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364

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

The HCF of 364,208 is 52.

Lets's calculate GCF of 364,208

Greatest Common Factor (GCF) of 364,208 By Common Division

2	364, 208
2	182, 104
13	91, 52
	7, 4

∴ So the GCF of the given numbers is 2 x 2 x 13 = 52

Greatest Common Factor of 364,208 By Matching Biggest Common Factor Method

Now, list down the factors of 364

1,2,4,7,13,14,26,28,52,91,182,364

Now, list down the factors of 208

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

Greatest Common Factor

We found the factors 364,208 . The biggest common factor number is the GCF number.
So the greatest common factor 364,208 is 52.

Lets's calculate LCM of 128,846

Lowest Common Multiple of 128,846 using Common Division

2	128, 846
	64, 423

∴ So the LCM of the given numbers is 2 x 64 x 423 = 54144

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 52/54144

Therefore, the GCF of Fractions 364/128,208/846 is 52/54144

Least Common Multiple of 128,846 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 128,846 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(128,846) = 2

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

GCF(128,846) x common factors =2 x 1 = 2

LCM(128,846) = ( 128 × 846 ) / 2

LCM(128,846) = 108288 / 2

LCM(128,846) = 54144

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FAQs on GCF of Fractions of 364/128, 208/846

1. What is the HCF of 364,208?

The HCF of 364,208 is 52

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 364/128, 208/846?

Answer: GCF of Numerators as per given numbers 364/128, 208/846 is

GCF of Numerators i.e. for 364,208 is 52

LCM of denominators i.e. for 128,846 is 54144.

Thus, GCF of Fractions is 52/54144.Finally, GCF of Fractions for 364/128, 208/846 is 52/54144.