How to Find GCF of 6689/900, 7869/584?

GCF of 6689/900, 7869/584

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 6689/900, 7869/584 i.e 1/131400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6689/900, 7869/584.

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 6689/900,7869/584?

Given fractions are 6689/900,7869/584

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 6689/900,7869/584, numerators are 6689,7869

Denominators are 900,584

The GCF of 6689,7869 is 1 .

LCM of 900,584 is 131400.

The greatest common factor of 6689/900,7869/584 = [GCF of 6689,7869]/[LCM of 900,584]= 1/131400

Therefore, the GCF of 6689/900,7869/584 is 1/131400.

Greatest Common Factor of 6689,7869

To find the highest common factor of 6689,7869, we have to find the factors of both numbers and list the highest common factor.

The factors of 6689 are 1, 6689

The factors of 7869 are 1, 3, 43, 61, 129, 183, 2623, 7869

The HCF of 6689,7869 is 1.

Lets's calculate GCF of 6689,7869

Greatest Common Factor (GCF) of 6689,7869 By Common Division

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

Greatest Common Factor of 6689,7869 By Matching Biggest Common Factor Method

Now, list down the factors of 6689

1,6689

Now, list down the factors of 7869

1,3,43,61,129,183,2623,7869

Greatest Common Factor

We found the factors 6689,7869 . The biggest common factor number is the GCF number.
So the greatest common factor 6689,7869 is 1.

Lets's calculate LCM of 900,584

Lowest Common Multiple of 900,584 using Common Division

2	900, 584
2	450, 292
	225, 146

∴ So the LCM of the given numbers is 2 x 2 x 225 x 146 = 131400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/131400

Therefore, the GCF of Fractions 6689/900,7869/584 is 1/131400

Least Common Multiple of 900,584 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 900,584 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(900,584) = 4

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

GCF(900,584) x common factors =4 x 1 = 4

LCM(900,584) = ( 900 × 584 ) / 4

LCM(900,584) = 525600 / 4

LCM(900,584) = 131400

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FAQs on GCF of Fractions of 6689/900, 7869/584

1. What is the HCF of 6689,7869?

The HCF of 6689,7869 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 6689/900, 7869/584?

Answer: GCF of Numerators as per given numbers 6689/900, 7869/584 is

GCF of Numerators i.e. for 6689,7869 is 1

LCM of denominators i.e. for 900,584 is 131400.

Thus, GCF of Fractions is 1/131400.Finally, GCF of Fractions for 6689/900, 7869/584 is 1/131400.