How to Find GCF of 256/224, 3826/232?

GCF of 256/224, 3826/232

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 256/224, 3826/232 i.e 2/6496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 256/224, 3826/232.

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 256/224,3826/232?

Given fractions are 256/224,3826/232

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 256/224,3826/232, numerators are 256,3826

Denominators are 224,232

The GCF of 256,3826 is 2 .

LCM of 224,232 is 6496.

The greatest common factor of 256/224,3826/232 = [GCF of 256,3826]/[LCM of 224,232]= 2/6496

Therefore, the GCF of 256/224,3826/232 is 2/6496.

Greatest Common Factor of 256,3826

To find the highest common factor of 256,3826, we have to find the factors of both numbers and list the highest common factor.

The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256

The factors of 3826 are 1, 2, 1913, 3826

The HCF of 256,3826 is 2.

Lets's calculate GCF of 256,3826

Greatest Common Factor (GCF) of 256,3826 By Common Division

2	256, 3826
	128, 1913

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

Greatest Common Factor of 256,3826 By Matching Biggest Common Factor Method

Now, list down the factors of 256

1,2,4,8,16,32,64,128,256

Now, list down the factors of 3826

1,2,1913,3826

Greatest Common Factor

We found the factors 256,3826 . The biggest common factor number is the GCF number.
So the greatest common factor 256,3826 is 2.

Lets's calculate LCM of 224,232

Lowest Common Multiple of 224,232 using Common Division

2	224, 232
2	112, 116
2	56, 58
	28, 29

∴ So the LCM of the given numbers is 2 x 2 x 2 x 28 x 29 = 6496

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6496

Therefore, the GCF of Fractions 256/224,3826/232 is 2/6496

Least Common Multiple of 224,232 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 224,232 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(224,232) = 8

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

GCF(224,232) x common factors =8 x 1 = 8

LCM(224,232) = ( 224 × 232 ) / 8

LCM(224,232) = 51968 / 8

LCM(224,232) = 6496

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FAQs on GCF of Fractions of 256/224, 3826/232

1. What is the HCF of 256,3826?

The HCF of 256,3826 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 256/224, 3826/232?

Answer: GCF of Numerators as per given numbers 256/224, 3826/232 is

GCF of Numerators i.e. for 256,3826 is 2

LCM of denominators i.e. for 224,232 is 6496.

Thus, GCF of Fractions is 2/6496.Finally, GCF of Fractions for 256/224, 3826/232 is 2/6496.