How to Find GCF of 9688/256, 3406/5290?

GCF of 9688/256, 3406/5290

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 9688/256, 3406/5290 i.e 2/677120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9688/256, 3406/5290.

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 9688/256,3406/5290?

Given fractions are 9688/256,3406/5290

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 9688/256,3406/5290, numerators are 9688,3406

Denominators are 256,5290

The GCF of 9688,3406 is 2 .

LCM of 256,5290 is 677120.

The greatest common factor of 9688/256,3406/5290 = [GCF of 9688,3406]/[LCM of 256,5290]= 2/677120

Therefore, the GCF of 9688/256,3406/5290 is 2/677120.

Greatest Common Factor of 9688,3406

To find the highest common factor of 9688,3406, we have to find the factors of both numbers and list the highest common factor.

The factors of 9688 are 1, 2, 4, 7, 8, 14, 28, 56, 173, 346, 692, 1211, 1384, 2422, 4844, 9688

The factors of 3406 are 1, 2, 13, 26, 131, 262, 1703, 3406

The HCF of 9688,3406 is 2.

Lets's calculate GCF of 9688,3406

Greatest Common Factor (GCF) of 9688,3406 By Common Division

2	9688, 3406
	4844, 1703

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

Greatest Common Factor of 9688,3406 By Matching Biggest Common Factor Method

Now, list down the factors of 9688

1,2,4,7,8,14,28,56,173,346,692,1211,1384,2422,4844,9688

Now, list down the factors of 3406

1,2,13,26,131,262,1703,3406

Greatest Common Factor

We found the factors 9688,3406 . The biggest common factor number is the GCF number.
So the greatest common factor 9688,3406 is 2.

Lets's calculate LCM of 256,5290

Lowest Common Multiple of 256,5290 using Common Division

2	256, 5290
	128, 2645

∴ So the LCM of the given numbers is 2 x 128 x 2645 = 677120

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/677120

Therefore, the GCF of Fractions 9688/256,3406/5290 is 2/677120

Least Common Multiple of 256,5290 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 256,5290 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(256,5290) = 2

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

GCF(256,5290) x common factors =2 x 1 = 2

LCM(256,5290) = ( 256 × 5290 ) / 2

LCM(256,5290) = 1354240 / 2

LCM(256,5290) = 677120

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 9688/256, 3406/5290

1. What is the HCF of 9688,3406?

The HCF of 9688,3406 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 9688/256, 3406/5290?

Answer: GCF of Numerators as per given numbers 9688/256, 3406/5290 is

GCF of Numerators i.e. for 9688,3406 is 2

LCM of denominators i.e. for 256,5290 is 677120.

Thus, GCF of Fractions is 2/677120.Finally, GCF of Fractions for 9688/256, 3406/5290 is 2/677120.