How to Find GCF of 689/760, 384/864?

GCF of 689/760, 384/864

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 689/760, 384/864 i.e 1/82080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 689/760, 384/864.

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 689/760,384/864?

Given fractions are 689/760,384/864

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 689/760,384/864, numerators are 689,384

Denominators are 760,864

The GCF of 689,384 is 1 .

LCM of 760,864 is 82080.

The greatest common factor of 689/760,384/864 = [GCF of 689,384]/[LCM of 760,864]= 1/82080

Therefore, the GCF of 689/760,384/864 is 1/82080.

Greatest Common Factor of 689,384

To find the highest common factor of 689,384, we have to find the factors of both numbers and list the highest common factor.

The factors of 689 are 1, 13, 53, 689

The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384

The HCF of 689,384 is 1.

Lets's calculate GCF of 689,384

Greatest Common Factor (GCF) of 689,384 By Common Division

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

Greatest Common Factor of 689,384 By Matching Biggest Common Factor Method

Now, list down the factors of 689

1,13,53,689

Now, list down the factors of 384

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384

Greatest Common Factor

We found the factors 689,384 . The biggest common factor number is the GCF number.
So the greatest common factor 689,384 is 1.

Lets's calculate LCM of 760,864

Lowest Common Multiple of 760,864 using Common Division

2	760, 864
2	380, 432
2	190, 216
	95, 108

∴ So the LCM of the given numbers is 2 x 2 x 2 x 95 x 108 = 82080

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/82080

Therefore, the GCF of Fractions 689/760,384/864 is 1/82080

Least Common Multiple of 760,864 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 760,864 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(760,864) = 8

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

GCF(760,864) x common factors =8 x 1 = 8

LCM(760,864) = ( 760 × 864 ) / 8

LCM(760,864) = 656640 / 8

LCM(760,864) = 82080

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FAQs on GCF of Fractions of 689/760, 384/864

1. What is the HCF of 689,384?

The HCF of 689,384 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 689/760, 384/864?

Answer: GCF of Numerators as per given numbers 689/760, 384/864 is

GCF of Numerators i.e. for 689,384 is 1

LCM of denominators i.e. for 760,864 is 82080.

Thus, GCF of Fractions is 1/82080.Finally, GCF of Fractions for 689/760, 384/864 is 1/82080.