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GCF of 290/687, 705/512

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 290/687, 705/512 i.e 5/351744 easily. The following is the detailed procedure to determine the greatest common factor of fractions 290/687, 705/512.

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 290/687,705/512?

Given fractions are 290/687,705/512

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 290/687,705/512, numerators are 290,705

Denominators are 687,512

The GCF of 290,705 is 5 .

LCM of 687,512 is 351744.

The greatest common factor of 290/687,705/512 = [GCF of 290,705]/[LCM of 687,512]= 5/351744

Therefore, the GCF of 290/687,705/512 is 5/351744.

Greatest Common Factor of 290,705

To find the highest common factor of 290,705, we have to find the factors of both numbers and list the highest common factor.

The factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290

The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705

The HCF of 290,705 is 5.

Lets's calculate GCF of 290,705

Greatest Common Factor (GCF) of 290,705 By Common Division

5 290, 705
58, 141

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 290,705 By Matching Biggest Common Factor Method

Greatest Common Factor of 290,705 By Matching Biggest Common Factor Method

Now, list down the factors of 290

:

1,2,5,10,29,58,145,290

Now, list down the factors of 705

:

1,3,5,15,47,141,235,705

Greatest Common Factor

We found the factors 290,705 . The biggest common factor number is the GCF number.
So the greatest common factor 290,705 is 5.

Lets's calculate LCM of 687,512

Lowest Common Multiple of 687,512 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 351744

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/351744

Therefore, the GCF of Fractions 290/687,705/512 is 5/351744

Least Common Multiple of 687,512 with GCF Formula

Least Common Multiple of 687,512 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 687,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(687,512) = 1

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

GCF(687,512) x common factors =1 x 1 = 1

LCM(687,512) = ( 687 × 512 ) / 1

LCM(687,512) = 351744 / 1

LCM(687,512) = 351744


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FAQs on GCF of Fractions of 290/687, 705/512

1. What is the HCF of 290,705?

The HCF of 290,705 is 5

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 290/687, 705/512?

Answer: GCF of Numerators as per given numbers 290/687, 705/512 is

GCF of Numerators i.e. for 290,705 is 5

LCM of denominators i.e. for 687,512 is 351744.

Thus, GCF of Fractions is 5/351744.Finally, GCF of Fractions for 290/687, 705/512 is 5/351744.