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GCF of 766/688, 589/580

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 766/688, 589/580 i.e 1/99760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 766/688, 589/580.

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 766/688,589/580?

Given fractions are 766/688,589/580

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 766/688,589/580, numerators are 766,589

Denominators are 688,580

The GCF of 766,589 is 1 .

LCM of 688,580 is 99760.

The greatest common factor of 766/688,589/580 = [GCF of 766,589]/[LCM of 688,580]= 1/99760

Therefore, the GCF of 766/688,589/580 is 1/99760.

Greatest Common Factor of 766,589

To find the highest common factor of 766,589, we have to find the factors of both numbers and list the highest common factor.

The factors of 766 are 1, 2, 383, 766

The factors of 589 are 1, 19, 31, 589

The HCF of 766,589 is 1.

Lets's calculate GCF of 766,589

Greatest Common Factor (GCF) of 766,589 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 766,589 By Matching Biggest Common Factor Method

Greatest Common Factor of 766,589 By Matching Biggest Common Factor Method

Now, list down the factors of 766

:

1,2,383,766

Now, list down the factors of 589

:

1,19,31,589

Greatest Common Factor

We found the factors 766,589 . The biggest common factor number is the GCF number.
So the greatest common factor 766,589 is 1.

Lets's calculate LCM of 688,580

Lowest Common Multiple of 688,580 using Common Division

2 688, 580
2 344, 290
172, 145

∴ So the LCM of the given numbers is 2 x 2 x 172 x 145 = 99760

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/99760

Therefore, the GCF of Fractions 766/688,589/580 is 1/99760

Least Common Multiple of 688,580 with GCF Formula

Least Common Multiple of 688,580 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 688,580 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(688,580) = 4

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

GCF(688,580) x common factors =4 x 1 = 4

LCM(688,580) = ( 688 × 580 ) / 4

LCM(688,580) = 399040 / 4

LCM(688,580) = 99760


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FAQs on GCF of Fractions of 766/688, 589/580

1. What is the HCF of 766,589?

The HCF of 766,589 is 1

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 766/688, 589/580?

Answer: GCF of Numerators as per given numbers 766/688, 589/580 is

GCF of Numerators i.e. for 766,589 is 1

LCM of denominators i.e. for 688,580 is 99760.

Thus, GCF of Fractions is 1/99760.Finally, GCF of Fractions for 766/688, 589/580 is 1/99760.