How to Find GCF of 7189/416, 3302/5416?

GCF of 7189/416, 3302/5416

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 7189/416, 3302/5416 i.e 13/281632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7189/416, 3302/5416.

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 7189/416,3302/5416?

Given fractions are 7189/416,3302/5416

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 7189/416,3302/5416, numerators are 7189,3302

Denominators are 416,5416

The GCF of 7189,3302 is 13 .

LCM of 416,5416 is 281632.

The greatest common factor of 7189/416,3302/5416 = [GCF of 7189,3302]/[LCM of 416,5416]= 13/281632

Therefore, the GCF of 7189/416,3302/5416 is 13/281632.

Greatest Common Factor of 7189,3302

To find the highest common factor of 7189,3302, we have to find the factors of both numbers and list the highest common factor.

The factors of 7189 are 1, 7, 13, 79, 91, 553, 1027, 7189

The factors of 3302 are 1, 2, 13, 26, 127, 254, 1651, 3302

The HCF of 7189,3302 is 13.

Lets's calculate GCF of 7189,3302

Greatest Common Factor (GCF) of 7189,3302 By Common Division

13	7189, 3302
	553, 254

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 7189,3302 By Matching Biggest Common Factor Method

Now, list down the factors of 7189

1,7,13,79,91,553,1027,7189

Now, list down the factors of 3302

1,2,13,26,127,254,1651,3302

Greatest Common Factor

We found the factors 7189,3302 . The biggest common factor number is the GCF number.
So the greatest common factor 7189,3302 is 13.

Lets's calculate LCM of 416,5416

Lowest Common Multiple of 416,5416 using Common Division

2	416, 5416
2	208, 2708
2	104, 1354
	52, 677

∴ So the LCM of the given numbers is 2 x 2 x 2 x 52 x 677 = 281632

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/281632

Therefore, the GCF of Fractions 7189/416,3302/5416 is 13/281632

Least Common Multiple of 416,5416 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 416,5416 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(416,5416) = 8

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

GCF(416,5416) x common factors =8 x 1 = 8

LCM(416,5416) = ( 416 × 5416 ) / 8

LCM(416,5416) = 2253056 / 8

LCM(416,5416) = 281632

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FAQs on GCF of Fractions of 7189/416, 3302/5416

1. What is the HCF of 7189,3302?

The HCF of 7189,3302 is 13

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 7189/416, 3302/5416?

Answer: GCF of Numerators as per given numbers 7189/416, 3302/5416 is

GCF of Numerators i.e. for 7189,3302 is 13

LCM of denominators i.e. for 416,5416 is 281632.

Thus, GCF of Fractions is 13/281632.Finally, GCF of Fractions for 7189/416, 3302/5416 is 13/281632.