How to Find GCF of 682/732, 9982/380?

GCF of 682/732, 9982/380

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 682/732, 9982/380 i.e 62/69540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 682/732, 9982/380.

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 682/732,9982/380?

Given fractions are 682/732,9982/380

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 682/732,9982/380, numerators are 682,9982

Denominators are 732,380

The GCF of 682,9982 is 62 .

LCM of 732,380 is 69540.

The greatest common factor of 682/732,9982/380 = [GCF of 682,9982]/[LCM of 732,380]= 62/69540

Therefore, the GCF of 682/732,9982/380 is 62/69540.

Greatest Common Factor of 682,9982

To find the highest common factor of 682,9982, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 9982 are 1, 2, 7, 14, 23, 31, 46, 62, 161, 217, 322, 434, 713, 1426, 4991, 9982

The HCF of 682,9982 is 62.

Lets's calculate GCF of 682,9982

Greatest Common Factor (GCF) of 682,9982 By Common Division

2	682, 9982
31	341, 4991
	11, 161

∴ So the GCF of the given numbers is 2 x 31 = 62

Greatest Common Factor of 682,9982 By Matching Biggest Common Factor Method

Now, list down the factors of 682

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

Now, list down the factors of 9982

1,2,7,14,23,31,46,62,161,217,322,434,713,1426,4991,9982

Greatest Common Factor

We found the factors 682,9982 . The biggest common factor number is the GCF number.
So the greatest common factor 682,9982 is 62.

Lets's calculate LCM of 732,380

Lowest Common Multiple of 732,380 using Common Division

2	732, 380
2	366, 190
	183, 95

∴ So the LCM of the given numbers is 2 x 2 x 183 x 95 = 69540

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 62/69540

Therefore, the GCF of Fractions 682/732,9982/380 is 62/69540

Least Common Multiple of 732,380 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 732,380 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(732,380) = 4

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

GCF(732,380) x common factors =4 x 1 = 4

LCM(732,380) = ( 732 × 380 ) / 4

LCM(732,380) = 278160 / 4

LCM(732,380) = 69540

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FAQs on GCF of Fractions of 682/732, 9982/380

1. What is the HCF of 682,9982?

The HCF of 682,9982 is 62

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 682/732, 9982/380?

Answer: GCF of Numerators as per given numbers 682/732, 9982/380 is

GCF of Numerators i.e. for 682,9982 is 62

LCM of denominators i.e. for 732,380 is 69540.

Thus, GCF of Fractions is 62/69540.Finally, GCF of Fractions for 682/732, 9982/380 is 62/69540.