How to Find GCF of 216/394, 748/721?

GCF of 216/394, 748/721

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 216/394, 748/721 i.e 4/284074 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/394, 748/721.

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 216/394,748/721?

Given fractions are 216/394,748/721

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 216/394,748/721, numerators are 216,748

Denominators are 394,721

The GCF of 216,748 is 4 .

LCM of 394,721 is 284074.

The greatest common factor of 216/394,748/721 = [GCF of 216,748]/[LCM of 394,721]= 4/284074

Therefore, the GCF of 216/394,748/721 is 4/284074.

Greatest Common Factor of 216,748

To find the highest common factor of 216,748, we have to find the factors of both numbers and list the highest common factor.

The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748

The HCF of 216,748 is 4.

Lets's calculate GCF of 216,748

Greatest Common Factor (GCF) of 216,748 By Common Division

2	216, 748
2	108, 374
	54, 187

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 216,748 By Matching Biggest Common Factor Method

Now, list down the factors of 216

1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216

Now, list down the factors of 748

1,2,4,11,17,22,34,44,68,187,374,748

Greatest Common Factor

We found the factors 216,748 . The biggest common factor number is the GCF number.
So the greatest common factor 216,748 is 4.

Lets's calculate LCM of 394,721

Lowest Common Multiple of 394,721 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 284074

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/284074

Therefore, the GCF of Fractions 216/394,748/721 is 4/284074

Least Common Multiple of 394,721 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 394,721 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(394,721) = 1

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

GCF(394,721) x common factors =1 x 1 = 1

LCM(394,721) = ( 394 × 721 ) / 1

LCM(394,721) = 284074 / 1

LCM(394,721) = 284074

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FAQs on GCF of Fractions of 216/394, 748/721

1. What is the HCF of 216,748?

The HCF of 216,748 is 4

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 216/394, 748/721?

Answer: GCF of Numerators as per given numbers 216/394, 748/721 is

GCF of Numerators i.e. for 216,748 is 4

LCM of denominators i.e. for 394,721 is 284074.

Thus, GCF of Fractions is 4/284074.Finally, GCF of Fractions for 216/394, 748/721 is 4/284074.