How to Find GCF of 14/231, 16/600, 197/952?

GCF of 14/231, 16/600, 197/952

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 14/231, 16/600, 197/952 i.e 1/785400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/231, 16/600, 197/952.

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 14/231,16/600,197/952?

Given fractions are 14/231,16/600,197/952

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 14/231,16/600,197/952, numerators are 14,16,197

Denominators are 231,600,952

The GCF of 14,16,197 is 1 .

LCM of 231,600,952 is 785400.

The greatest common factor of 14/231,16/600,197/952 = [GCF of 14,16,197]/[LCM of 231,600,952]= 1/785400

Therefore, the GCF of 14/231,16/600,197/952 is 1/785400.

Greatest Common Factor of 14,16,197

To find the highest common factor of 14,16,197, we have to find the factors of both numbers and list the highest common factor.

The factors of 14 are 1, 2, 7, 14

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

The factors of 197 are 1, 197

The HCF of 14,16,197 is 1.

Lets's calculate GCF of 14,16,197

Greatest Common Factor (GCF) of 14,16,197 By Common Division

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

Greatest Common Factor of 14,16,197 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 16

1,2,4,8,16

Now, list down the factors of 197

1,197

Greatest Common Factor

We found the factors 14,16,197 . The biggest common factor number is the GCF number.
So the greatest common factor 14,16,197 is 1.

Lets's calculate LCM of 231,600,952

Lowest Common Multiple of 231,600,952 using Common Division

2	231, 600, 952
2	231, 300, 476
2	231, 150, 238
3	231, 75, 119
7	77, 25, 119
	11, 25, 17

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 7 x 11 x 25 x 17 = 785400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/785400

Therefore, the GCF of Fractions 14/231,16/600,197/952 is 1/785400

Least Common Multiple of 231,600,952 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 231,600,952 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(231,600,952) = 1

common factors(in case of two or more numbers have common factors) = 168

GCF(231,600,952) x common factors =1 x 168 = 168

LCM(231,600,952) = ( 231 × 600 × 952 ) / 168

LCM(231,600,952) = 131947200 / 168

LCM(231,600,952) = 785400

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 14/231, 16/600, 197/952

1. What is the HCF of 14,16,197?

The HCF of 14,16,197 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 14/231, 16/600, 197/952?

Answer: GCF of Numerators as per given numbers 14/231, 16/600, 197/952 is

GCF of Numerators i.e. for 14,16,197 is 1

LCM of denominators i.e. for 231,600,952 is 785400.

Thus, GCF of Fractions is 1/785400.Finally, GCF of Fractions for 14/231, 16/600, 197/952 is 1/785400.