How to Find GCF of 14/614, 32/516, 653/266?

GCF of 14/614, 32/516, 653/266

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 14/614, 32/516, 653/266 i.e 1/21068796 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/614, 32/516, 653/266.

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 14/614,32/516,653/266?

Given fractions are 14/614,32/516,653/266

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 14/614,32/516,653/266, numerators are 14,32,653

Denominators are 614,516,266

The GCF of 14,32,653 is 1 .

LCM of 614,516,266 is 21068796.

The greatest common factor of 14/614,32/516,653/266 = [GCF of 14,32,653]/[LCM of 614,516,266]= 1/21068796

Therefore, the GCF of 14/614,32/516,653/266 is 1/21068796.

Greatest Common Factor of 14,32,653

To find the highest common factor of 14,32,653, 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 32 are 1, 2, 4, 8, 16, 32

The factors of 653 are 1, 653

The HCF of 14,32,653 is 1.

Lets's calculate GCF of 14,32,653

Greatest Common Factor (GCF) of 14,32,653 By Common Division

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

Greatest Common Factor of 14,32,653 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 32

1,2,4,8,16,32

Now, list down the factors of 653

1,653

Greatest Common Factor

We found the factors 14,32,653 . The biggest common factor number is the GCF number.
So the greatest common factor 14,32,653 is 1.

Lets's calculate LCM of 614,516,266

Lowest Common Multiple of 614,516,266 using Common Division

2	614, 516, 266
	307, 258, 133

∴ So the LCM of the given numbers is 2 x 307 x 258 x 133 = 21068796

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21068796

Therefore, the GCF of Fractions 14/614,32/516,653/266 is 1/21068796

Least Common Multiple of 614,516,266 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 614,516,266 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(614,516,266) = 2

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

GCF(614,516,266) x common factors =2 x 2 = 4

LCM(614,516,266) = ( 614 × 516 × 266 ) / 4

LCM(614,516,266) = 84275184 / 4

LCM(614,516,266) = 21068796

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FAQs on GCF of Fractions of 14/614, 32/516, 653/266

1. What is the HCF of 14,32,653?

The HCF of 14,32,653 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 14/614, 32/516, 653/266?

Answer: GCF of Numerators as per given numbers 14/614, 32/516, 653/266 is

GCF of Numerators i.e. for 14,32,653 is 1

LCM of denominators i.e. for 614,516,266 is 21068796.

Thus, GCF of Fractions is 1/21068796.Finally, GCF of Fractions for 14/614, 32/516, 653/266 is 1/21068796.