How to Find GCF of 4172/188, 9728/108?

GCF of 4172/188, 9728/108

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 4172/188, 9728/108 i.e 4/5076 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4172/188, 9728/108.

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 4172/188,9728/108?

Given fractions are 4172/188,9728/108

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 4172/188,9728/108, numerators are 4172,9728

Denominators are 188,108

The GCF of 4172,9728 is 4 .

LCM of 188,108 is 5076.

The greatest common factor of 4172/188,9728/108 = [GCF of 4172,9728]/[LCM of 188,108]= 4/5076

Therefore, the GCF of 4172/188,9728/108 is 4/5076.

Greatest Common Factor of 4172,9728

To find the highest common factor of 4172,9728, we have to find the factors of both numbers and list the highest common factor.

The factors of 4172 are 1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086, 4172

The factors of 9728 are 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1216, 2432, 4864, 9728

The HCF of 4172,9728 is 4.

Lets's calculate GCF of 4172,9728

Greatest Common Factor (GCF) of 4172,9728 By Common Division

2	4172, 9728
2	2086, 4864
	1043, 2432

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 4172,9728 By Matching Biggest Common Factor Method

Now, list down the factors of 4172

1,2,4,7,14,28,149,298,596,1043,2086,4172

Now, list down the factors of 9728

1,2,4,8,16,19,32,38,64,76,128,152,256,304,512,608,1216,2432,4864,9728

Greatest Common Factor

We found the factors 4172,9728 . The biggest common factor number is the GCF number.
So the greatest common factor 4172,9728 is 4.

Lets's calculate LCM of 188,108

Lowest Common Multiple of 188,108 using Common Division

2	188, 108
2	94, 54
	47, 27

∴ So the LCM of the given numbers is 2 x 2 x 47 x 27 = 5076

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/5076

Therefore, the GCF of Fractions 4172/188,9728/108 is 4/5076

Least Common Multiple of 188,108 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 188,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(188,108) = 4

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

GCF(188,108) x common factors =4 x 1 = 4

LCM(188,108) = ( 188 × 108 ) / 4

LCM(188,108) = 20304 / 4

LCM(188,108) = 5076

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 4172/188, 9728/108

1. What is the HCF of 4172,9728?

The HCF of 4172,9728 is 4

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 4172/188, 9728/108?

Answer: GCF of Numerators as per given numbers 4172/188, 9728/108 is

GCF of Numerators i.e. for 4172,9728 is 4

LCM of denominators i.e. for 188,108 is 5076.

Thus, GCF of Fractions is 4/5076.Finally, GCF of Fractions for 4172/188, 9728/108 is 4/5076.