How to Find GCF of 723/74, 369/85, 348/13?

GCF of 723/74, 369/85, 348/13

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 723/74, 369/85, 348/13 i.e 3/81770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 723/74, 369/85, 348/13.

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 723/74,369/85,348/13?

Given fractions are 723/74,369/85,348/13

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 723/74,369/85,348/13, numerators are 723,369,348

Denominators are 74,85,13

The GCF of 723,369,348 is 3 .

LCM of 74,85,13 is 81770.

The greatest common factor of 723/74,369/85,348/13 = [GCF of 723,369,348]/[LCM of 74,85,13]= 3/81770

Therefore, the GCF of 723/74,369/85,348/13 is 3/81770.

Greatest Common Factor of 723,369,348

To find the highest common factor of 723,369,348, we have to find the factors of both numbers and list the highest common factor.

The factors of 723 are 1, 3, 241, 723

The factors of 369 are 1, 3, 9, 41, 123, 369

The factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348

The HCF of 723,369,348 is 3.

Lets's calculate GCF of 723,369,348

Greatest Common Factor (GCF) of 723,369,348 By Common Division

3	723, 369, 348
	241, 123, 116

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 723,369,348 By Matching Biggest Common Factor Method

Now, list down the factors of 723

1,3,241,723

Now, list down the factors of 369

1,3,9,41,123,369

Now, list down the factors of 348

1,2,3,4,6,12,29,58,87,116,174,348

Greatest Common Factor

We found the factors 723,369,348 . The biggest common factor number is the GCF number.
So the greatest common factor 723,369,348 is 3.

Lets's calculate LCM of 74,85,13

Lowest Common Multiple of 74,85,13 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 81770

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/81770

Therefore, the GCF of Fractions 723/74,369/85,348/13 is 3/81770

Least Common Multiple of 74,85,13 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 74,85,13 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(74,85,13) = 1

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

GCF(74,85,13) x common factors =1 x 1 = 1

LCM(74,85,13) = ( 74 × 85 × 13 ) / 1

LCM(74,85,13) = 81770 / 1

LCM(74,85,13) = 81770

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 723/74, 369/85, 348/13

1. What is the HCF of 723,369,348?

The HCF of 723,369,348 is 3

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 723/74, 369/85, 348/13?

Answer: GCF of Numerators as per given numbers 723/74, 369/85, 348/13 is

GCF of Numerators i.e. for 723,369,348 is 3

LCM of denominators i.e. for 74,85,13 is 81770.

Thus, GCF of Fractions is 3/81770.Finally, GCF of Fractions for 723/74, 369/85, 348/13 is 3/81770.