How to Find GCF of 38/256, 7654/7256?

GCF of 38/256, 7654/7256

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 38/256, 7654/7256 i.e 2/232192 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/256, 7654/7256.

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 38/256,7654/7256?

Given fractions are 38/256,7654/7256

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 38/256,7654/7256, numerators are 38,7654

Denominators are 256,7256

The GCF of 38,7654 is 2 .

LCM of 256,7256 is 232192.

The greatest common factor of 38/256,7654/7256 = [GCF of 38,7654]/[LCM of 256,7256]= 2/232192

Therefore, the GCF of 38/256,7654/7256 is 2/232192.

Greatest Common Factor of 38,7654

To find the highest common factor of 38,7654, we have to find the factors of both numbers and list the highest common factor.

The factors of 38 are 1, 2, 19, 38

The factors of 7654 are 1, 2, 43, 86, 89, 178, 3827, 7654

The HCF of 38,7654 is 2.

Lets's calculate GCF of 38,7654

Greatest Common Factor (GCF) of 38,7654 By Common Division

2	38, 7654
	19, 3827

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

Greatest Common Factor of 38,7654 By Matching Biggest Common Factor Method

Now, list down the factors of 38

1,2,19,38

Now, list down the factors of 7654

1,2,43,86,89,178,3827,7654

Greatest Common Factor

We found the factors 38,7654 . The biggest common factor number is the GCF number.
So the greatest common factor 38,7654 is 2.

Lets's calculate LCM of 256,7256

Lowest Common Multiple of 256,7256 using Common Division

2	256, 7256
2	128, 3628
2	64, 1814
	32, 907

∴ So the LCM of the given numbers is 2 x 2 x 2 x 32 x 907 = 232192

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/232192

Therefore, the GCF of Fractions 38/256,7654/7256 is 2/232192

Least Common Multiple of 256,7256 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 256,7256 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(256,7256) = 8

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

GCF(256,7256) x common factors =8 x 1 = 8

LCM(256,7256) = ( 256 × 7256 ) / 8

LCM(256,7256) = 1857536 / 8

LCM(256,7256) = 232192

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FAQs on GCF of Fractions of 38/256, 7654/7256

1. What is the HCF of 38,7654?

The HCF of 38,7654 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 38/256, 7654/7256?

Answer: GCF of Numerators as per given numbers 38/256, 7654/7256 is

GCF of Numerators i.e. for 38,7654 is 2

LCM of denominators i.e. for 256,7256 is 232192.

Thus, GCF of Fractions is 2/232192.Finally, GCF of Fractions for 38/256, 7654/7256 is 2/232192.