How to Find GCF of 128/84, 272/6286?

GCF of 128/84, 272/6286

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 128/84, 272/6286 i.e 16/37716 easily. The following is the detailed procedure to determine the greatest common factor of fractions 128/84, 272/6286.

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 128/84,272/6286?

Given fractions are 128/84,272/6286

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 128/84,272/6286, numerators are 128,272

Denominators are 84,6286

The GCF of 128,272 is 16 .

LCM of 84,6286 is 37716.

The greatest common factor of 128/84,272/6286 = [GCF of 128,272]/[LCM of 84,6286]= 16/37716

Therefore, the GCF of 128/84,272/6286 is 16/37716.

Greatest Common Factor of 128,272

To find the highest common factor of 128,272, we have to find the factors of both numbers and list the highest common factor.

The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128

The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272

The HCF of 128,272 is 16.

Lets's calculate GCF of 128,272

Greatest Common Factor (GCF) of 128,272 By Common Division

2	128, 272
2	64, 136
2	32, 68
2	16, 34
	8, 17

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 128,272 By Matching Biggest Common Factor Method

Now, list down the factors of 128

1,2,4,8,16,32,64,128

Now, list down the factors of 272

1,2,4,8,16,17,34,68,136,272

Greatest Common Factor

We found the factors 128,272 . The biggest common factor number is the GCF number.
So the greatest common factor 128,272 is 16.

Lets's calculate LCM of 84,6286

Lowest Common Multiple of 84,6286 using Common Division

2	84, 6286
7	42, 3143
	6, 449

∴ So the LCM of the given numbers is 2 x 7 x 6 x 449 = 37716

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/37716

Therefore, the GCF of Fractions 128/84,272/6286 is 16/37716

Least Common Multiple of 84,6286 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 84,6286 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(84,6286) = 14

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

GCF(84,6286) x common factors =14 x 1 = 14

LCM(84,6286) = ( 84 × 6286 ) / 14

LCM(84,6286) = 528024 / 14

LCM(84,6286) = 37716

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FAQs on GCF of Fractions of 128/84, 272/6286

1. What is the HCF of 128,272?

The HCF of 128,272 is 16

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 128/84, 272/6286?

Answer: GCF of Numerators as per given numbers 128/84, 272/6286 is

GCF of Numerators i.e. for 128,272 is 16

LCM of denominators i.e. for 84,6286 is 37716.

Thus, GCF of Fractions is 16/37716.Finally, GCF of Fractions for 128/84, 272/6286 is 16/37716.