How to Find GCF of 726/299, 8382/364?

GCF of 726/299, 8382/364

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 726/299, 8382/364 i.e 66/8372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 726/299, 8382/364.

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 726/299,8382/364?

Given fractions are 726/299,8382/364

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 726/299,8382/364, numerators are 726,8382

Denominators are 299,364

The GCF of 726,8382 is 66 .

LCM of 299,364 is 8372.

The greatest common factor of 726/299,8382/364 = [GCF of 726,8382]/[LCM of 299,364]= 66/8372

Therefore, the GCF of 726/299,8382/364 is 66/8372.

Greatest Common Factor of 726,8382

To find the highest common factor of 726,8382, we have to find the factors of both numbers and list the highest common factor.

The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726

The factors of 8382 are 1, 2, 3, 6, 11, 22, 33, 66, 127, 254, 381, 762, 1397, 2794, 4191, 8382

The HCF of 726,8382 is 66.

Lets's calculate GCF of 726,8382

Greatest Common Factor (GCF) of 726,8382 By Common Division

2	726, 8382
3	363, 4191
11	121, 1397
	11, 127

∴ So the GCF of the given numbers is 2 x 3 x 11 = 66

Greatest Common Factor of 726,8382 By Matching Biggest Common Factor Method

Now, list down the factors of 726

1,2,3,6,11,22,33,66,121,242,363,726

Now, list down the factors of 8382

1,2,3,6,11,22,33,66,127,254,381,762,1397,2794,4191,8382

Greatest Common Factor

We found the factors 726,8382 . The biggest common factor number is the GCF number.
So the greatest common factor 726,8382 is 66.

Lets's calculate LCM of 299,364

Lowest Common Multiple of 299,364 using Common Division

13	299, 364
	23, 28

∴ So the LCM of the given numbers is 13 x 23 x 28 = 8372

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 66/8372

Therefore, the GCF of Fractions 726/299,8382/364 is 66/8372

Least Common Multiple of 299,364 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 299,364 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(299,364) = 13

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

GCF(299,364) x common factors =13 x 1 = 13

LCM(299,364) = ( 299 × 364 ) / 13

LCM(299,364) = 108836 / 13

LCM(299,364) = 8372

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FAQs on GCF of Fractions of 726/299, 8382/364

1. What is the HCF of 726,8382?

The HCF of 726,8382 is 66

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 726/299, 8382/364?

Answer: GCF of Numerators as per given numbers 726/299, 8382/364 is

GCF of Numerators i.e. for 726,8382 is 66

LCM of denominators i.e. for 299,364 is 8372.

Thus, GCF of Fractions is 66/8372.Finally, GCF of Fractions for 726/299, 8382/364 is 66/8372.