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GCF of 382/57, 416/289

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 382/57, 416/289 i.e 2/16473 easily. The following is the detailed procedure to determine the greatest common factor of fractions 382/57, 416/289.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 382/57,416/289?

Given fractions are 382/57,416/289

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 382/57,416/289, numerators are 382,416

Denominators are 57,289

The GCF of 382,416 is 2 .

LCM of 57,289 is 16473.

The greatest common factor of 382/57,416/289 = [GCF of 382,416]/[LCM of 57,289]= 2/16473

Therefore, the GCF of 382/57,416/289 is 2/16473.

Greatest Common Factor of 382,416

To find the highest common factor of 382,416, we have to find the factors of both numbers and list the highest common factor.

The factors of 382 are 1, 2, 191, 382

The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

The HCF of 382,416 is 2.

Lets's calculate GCF of 382,416

Greatest Common Factor (GCF) of 382,416 By Common Division

2 382, 416
191, 208

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

Greatest Common Factor of 382,416 By Matching Biggest Common Factor Method

Greatest Common Factor of 382,416 By Matching Biggest Common Factor Method

Now, list down the factors of 382

:

1,2,191,382

Now, list down the factors of 416

:

1,2,4,8,13,16,26,32,52,104,208,416

Greatest Common Factor

We found the factors 382,416 . The biggest common factor number is the GCF number.
So the greatest common factor 382,416 is 2.

Lets's calculate LCM of 57,289

Lowest Common Multiple of 57,289 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 16473

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/16473

Therefore, the GCF of Fractions 382/57,416/289 is 2/16473

Least Common Multiple of 57,289 with GCF Formula

Least Common Multiple of 57,289 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 57,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(57,289) = 1

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

GCF(57,289) x common factors =1 x 1 = 1

LCM(57,289) = ( 57 × 289 ) / 1

LCM(57,289) = 16473 / 1

LCM(57,289) = 16473


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FAQs on GCF of Fractions of 382/57, 416/289

1. What is the HCF of 382,416?

The HCF of 382,416 is 2

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 382/57, 416/289?

Answer: GCF of Numerators as per given numbers 382/57, 416/289 is

GCF of Numerators i.e. for 382,416 is 2

LCM of denominators i.e. for 57,289 is 16473.

Thus, GCF of Fractions is 2/16473.Finally, GCF of Fractions for 382/57, 416/289 is 2/16473.