How to Find GCF of 23/489, 69/340, 322/452?

GCF of 23/489, 69/340, 322/452

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 23/489, 69/340, 322/452 i.e 23/18787380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 23/489, 69/340, 322/452.

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 23/489,69/340,322/452?

Given fractions are 23/489,69/340,322/452

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 23/489,69/340,322/452, numerators are 23,69,322

Denominators are 489,340,452

The GCF of 23,69,322 is 23 .

LCM of 489,340,452 is 18787380.

The greatest common factor of 23/489,69/340,322/452 = [GCF of 23,69,322]/[LCM of 489,340,452]= 23/18787380

Therefore, the GCF of 23/489,69/340,322/452 is 23/18787380.

Greatest Common Factor of 23,69,322

To find the highest common factor of 23,69,322, we have to find the factors of both numbers and list the highest common factor.

The factors of 23 are 1, 23

The factors of 69 are 1, 3, 23, 69

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

The HCF of 23,69,322 is 23.

Lets's calculate GCF of 23,69,322

Greatest Common Factor (GCF) of 23,69,322 By Common Division

23	23, 69, 322
	1, 3, 14

∴ So the GCF of the given numbers is 23 = 23

Greatest Common Factor of 23,69,322 By Matching Biggest Common Factor Method

Now, list down the factors of 23

1,23

Now, list down the factors of 69

1,3,23,69

Now, list down the factors of 322

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

Greatest Common Factor

We found the factors 23,69,322 . The biggest common factor number is the GCF number.
So the greatest common factor 23,69,322 is 23.

Lets's calculate LCM of 489,340,452

Lowest Common Multiple of 489,340,452 using Common Division

2	489, 340, 452
2	489, 170, 226
	489, 85, 113

∴ So the LCM of the given numbers is 2 x 2 x 489 x 85 x 113 = 18787380

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/18787380

Therefore, the GCF of Fractions 23/489,69/340,322/452 is 23/18787380

Least Common Multiple of 489,340,452 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 489,340,452 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(489,340,452) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(489,340,452) x common factors =1 x 4 = 4

LCM(489,340,452) = ( 489 × 340 × 452 ) / 4

LCM(489,340,452) = 75149520 / 4

LCM(489,340,452) = 18787380

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 23/489, 69/340, 322/452

1. What is the HCF of 23,69,322?

The HCF of 23,69,322 is 23

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 23/489, 69/340, 322/452?

Answer: GCF of Numerators as per given numbers 23/489, 69/340, 322/452 is

GCF of Numerators i.e. for 23,69,322 is 23

LCM of denominators i.e. for 489,340,452 is 18787380.

Thus, GCF of Fractions is 23/18787380.Finally, GCF of Fractions for 23/489, 69/340, 322/452 is 23/18787380.