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GCF of 688/233, 6226/205

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 688/233, 6226/205 i.e 2/47765 easily. The following is the detailed procedure to determine the greatest common factor of fractions 688/233, 6226/205.

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 688/233,6226/205?

Given fractions are 688/233,6226/205

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 688/233,6226/205, numerators are 688,6226

Denominators are 233,205

The GCF of 688,6226 is 2 .

LCM of 233,205 is 47765.

The greatest common factor of 688/233,6226/205 = [GCF of 688,6226]/[LCM of 233,205]= 2/47765

Therefore, the GCF of 688/233,6226/205 is 2/47765.

Greatest Common Factor of 688,6226

To find the highest common factor of 688,6226, we have to find the factors of both numbers and list the highest common factor.

The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688

The factors of 6226 are 1, 2, 11, 22, 283, 566, 3113, 6226

The HCF of 688,6226 is 2.

Lets's calculate GCF of 688,6226

Greatest Common Factor (GCF) of 688,6226 By Common Division

2 688, 6226
344, 3113

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

Greatest Common Factor of 688,6226 By Matching Biggest Common Factor Method

Greatest Common Factor of 688,6226 By Matching Biggest Common Factor Method

Now, list down the factors of 688

:

1,2,4,8,16,43,86,172,344,688

Now, list down the factors of 6226

:

1,2,11,22,283,566,3113,6226

Greatest Common Factor

We found the factors 688,6226 . The biggest common factor number is the GCF number.
So the greatest common factor 688,6226 is 2.

Lets's calculate LCM of 233,205

Lowest Common Multiple of 233,205 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 47765

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/47765

Therefore, the GCF of Fractions 688/233,6226/205 is 2/47765

Least Common Multiple of 233,205 with GCF Formula

Least Common Multiple of 233,205 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 233,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(233,205) = 1

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

GCF(233,205) x common factors =1 x 1 = 1

LCM(233,205) = ( 233 × 205 ) / 1

LCM(233,205) = 47765 / 1

LCM(233,205) = 47765


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 688/233, 6226/205

1. What is the HCF of 688,6226?

The HCF of 688,6226 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 688/233, 6226/205?

Answer: GCF of Numerators as per given numbers 688/233, 6226/205 is

GCF of Numerators i.e. for 688,6226 is 2

LCM of denominators i.e. for 233,205 is 47765.

Thus, GCF of Fractions is 2/47765.Finally, GCF of Fractions for 688/233, 6226/205 is 2/47765.