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GCF of 296/384, 338/960

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 296/384, 338/960 i.e 2/1920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 296/384, 338/960.

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 296/384,338/960?

Given fractions are 296/384,338/960

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 296/384,338/960, numerators are 296,338

Denominators are 384,960

The GCF of 296,338 is 2 .

LCM of 384,960 is 1920.

The greatest common factor of 296/384,338/960 = [GCF of 296,338]/[LCM of 384,960]= 2/1920

Therefore, the GCF of 296/384,338/960 is 2/1920.

Greatest Common Factor of 296,338

To find the highest common factor of 296,338, we have to find the factors of both numbers and list the highest common factor.

The factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296

The factors of 338 are 1, 2, 13, 26, 169, 338

The HCF of 296,338 is 2.

Lets's calculate GCF of 296,338

Greatest Common Factor (GCF) of 296,338 By Common Division

2 296, 338
148, 169

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

Greatest Common Factor of 296,338 By Matching Biggest Common Factor Method

Greatest Common Factor of 296,338 By Matching Biggest Common Factor Method

Now, list down the factors of 296

:

1,2,4,8,37,74,148,296

Now, list down the factors of 338

:

1,2,13,26,169,338

Greatest Common Factor

We found the factors 296,338 . The biggest common factor number is the GCF number.
So the greatest common factor 296,338 is 2.

Lets's calculate LCM of 384,960

Lowest Common Multiple of 384,960 using Common Division

2 384, 960
2 192, 480
2 96, 240
2 48, 120
2 24, 60
2 12, 30
3 6, 15
2, 5

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 2 x 5 = 1920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1920

Therefore, the GCF of Fractions 296/384,338/960 is 2/1920

Least Common Multiple of 384,960 with GCF Formula

Least Common Multiple of 384,960 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 384,960 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(384,960) = 192

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

GCF(384,960) x common factors =192 x 1 = 192

LCM(384,960) = ( 384 × 960 ) / 192

LCM(384,960) = 368640 / 192

LCM(384,960) = 1920


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FAQs on GCF of Fractions of 296/384, 338/960

1. What is the HCF of 296,338?

The HCF of 296,338 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 296/384, 338/960?

Answer: GCF of Numerators as per given numbers 296/384, 338/960 is

GCF of Numerators i.e. for 296,338 is 2

LCM of denominators i.e. for 384,960 is 1920.

Thus, GCF of Fractions is 2/1920.Finally, GCF of Fractions for 296/384, 338/960 is 2/1920.