How to Find GCF of 665/584, 682/323?

GCF of 665/584, 682/323

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 665/584, 682/323 i.e 1/188632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 665/584, 682/323.

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 665/584,682/323?

Given fractions are 665/584,682/323

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 665/584,682/323, numerators are 665,682

Denominators are 584,323

The GCF of 665,682 is 1 .

LCM of 584,323 is 188632.

The greatest common factor of 665/584,682/323 = [GCF of 665,682]/[LCM of 584,323]= 1/188632

Therefore, the GCF of 665/584,682/323 is 1/188632.

Greatest Common Factor of 665,682

To find the highest common factor of 665,682, we have to find the factors of both numbers and list the highest common factor.

The factors of 665 are 1, 5, 7, 19, 35, 95, 133, 665

The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682

The HCF of 665,682 is 1.

Lets's calculate GCF of 665,682

Greatest Common Factor (GCF) of 665,682 By Common Division

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

Greatest Common Factor of 665,682 By Matching Biggest Common Factor Method

Now, list down the factors of 665

1,5,7,19,35,95,133,665

Now, list down the factors of 682

1,2,11,22,31,62,341,682

Greatest Common Factor

We found the factors 665,682 . The biggest common factor number is the GCF number.
So the greatest common factor 665,682 is 1.

Lets's calculate LCM of 584,323

Lowest Common Multiple of 584,323 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 188632

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/188632

Therefore, the GCF of Fractions 665/584,682/323 is 1/188632

Least Common Multiple of 584,323 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 584,323 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(584,323) = 1

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

GCF(584,323) x common factors =1 x 1 = 1

LCM(584,323) = ( 584 × 323 ) / 1

LCM(584,323) = 188632 / 1

LCM(584,323) = 188632

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FAQs on GCF of Fractions of 665/584, 682/323

1. What is the HCF of 665,682?

The HCF of 665,682 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 665/584, 682/323?

Answer: GCF of Numerators as per given numbers 665/584, 682/323 is

GCF of Numerators i.e. for 665,682 is 1

LCM of denominators i.e. for 584,323 is 188632.

Thus, GCF of Fractions is 1/188632.Finally, GCF of Fractions for 665/584, 682/323 is 1/188632.