How to Find GCF of 494/14, 659/16, 322/78?

GCF of 494/14, 659/16, 322/78

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 494/14, 659/16, 322/78 i.e 1/4368 easily. The following is the detailed procedure to determine the greatest common factor of fractions 494/14, 659/16, 322/78.

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 494/14,659/16,322/78?

Given fractions are 494/14,659/16,322/78

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 494/14,659/16,322/78, numerators are 494,659,322

Denominators are 14,16,78

The GCF of 494,659,322 is 1 .

LCM of 14,16,78 is 4368.

The greatest common factor of 494/14,659/16,322/78 = [GCF of 494,659,322]/[LCM of 14,16,78]= 1/4368

Therefore, the GCF of 494/14,659/16,322/78 is 1/4368.

Greatest Common Factor of 494,659,322

To find the highest common factor of 494,659,322, we have to find the factors of both numbers and list the highest common factor.

The factors of 494 are 1, 2, 13, 19, 26, 38, 247, 494

The factors of 659 are 1, 659

The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322

The HCF of 494,659,322 is 1.

Lets's calculate GCF of 494,659,322

Greatest Common Factor (GCF) of 494,659,322 By Common Division

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

Greatest Common Factor of 494,659,322 By Matching Biggest Common Factor Method

Now, list down the factors of 494

1,2,13,19,26,38,247,494

Now, list down the factors of 659

1,659

Now, list down the factors of 322

1,2,7,14,23,46,161,322

Greatest Common Factor

We found the factors 494,659,322 . The biggest common factor number is the GCF number.
So the greatest common factor 494,659,322 is 1.

Lets's calculate LCM of 14,16,78

Lowest Common Multiple of 14,16,78 using Common Division

2	14, 16, 78
	7, 8, 39

∴ So the LCM of the given numbers is 2 x 7 x 8 x 39 = 4368

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4368

Therefore, the GCF of Fractions 494/14,659/16,322/78 is 1/4368

Least Common Multiple of 14,16,78 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 14,16,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,16,78) = 2

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

GCF(14,16,78) x common factors =2 x 2 = 4

LCM(14,16,78) = ( 14 × 16 × 78 ) / 4

LCM(14,16,78) = 17472 / 4

LCM(14,16,78) = 4368

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FAQs on GCF of Fractions of 494/14, 659/16, 322/78

1. What is the HCF of 494,659,322?

The HCF of 494,659,322 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 494/14, 659/16, 322/78?

Answer: GCF of Numerators as per given numbers 494/14, 659/16, 322/78 is

GCF of Numerators i.e. for 494,659,322 is 1

LCM of denominators i.e. for 14,16,78 is 4368.

Thus, GCF of Fractions is 1/4368.Finally, GCF of Fractions for 494/14, 659/16, 322/78 is 1/4368.