How to Find GCF of 66/65, 204/89, 829/839?

GCF of 66/65, 204/89, 829/839

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 66/65, 204/89, 829/839 i.e 1/4853615 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/65, 204/89, 829/839.

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 66/65,204/89,829/839?

Given fractions are 66/65,204/89,829/839

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 66/65,204/89,829/839, numerators are 66,204,829

Denominators are 65,89,839

The GCF of 66,204,829 is 1 .

LCM of 65,89,839 is 4853615.

The greatest common factor of 66/65,204/89,829/839 = [GCF of 66,204,829]/[LCM of 65,89,839]= 1/4853615

Therefore, the GCF of 66/65,204/89,829/839 is 1/4853615.

Greatest Common Factor of 66,204,829

To find the highest common factor of 66,204,829, we have to find the factors of both numbers and list the highest common factor.

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66

The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

The factors of 829 are 1, 829

The HCF of 66,204,829 is 1.

Lets's calculate GCF of 66,204,829

Greatest Common Factor (GCF) of 66,204,829 By Common Division

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

Greatest Common Factor of 66,204,829 By Matching Biggest Common Factor Method

Now, list down the factors of 66

1,2,3,6,11,22,33,66

Now, list down the factors of 204

1,2,3,4,6,12,17,34,51,68,102,204

Now, list down the factors of 829

1,829

Greatest Common Factor

We found the factors 66,204,829 . The biggest common factor number is the GCF number.
So the greatest common factor 66,204,829 is 1.

Lets's calculate LCM of 65,89,839

Lowest Common Multiple of 65,89,839 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 4853615

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4853615

Therefore, the GCF of Fractions 66/65,204/89,829/839 is 1/4853615

Least Common Multiple of 65,89,839 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 65,89,839 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,89,839) = 1

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

GCF(65,89,839) x common factors =1 x 1 = 1

LCM(65,89,839) = ( 65 × 89 × 839 ) / 1

LCM(65,89,839) = 4853615 / 1

LCM(65,89,839) = 4853615

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 66/65, 204/89, 829/839

1. What is the HCF of 66,204,829?

The HCF of 66,204,829 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 66/65, 204/89, 829/839?

Answer: GCF of Numerators as per given numbers 66/65, 204/89, 829/839 is

GCF of Numerators i.e. for 66,204,829 is 1

LCM of denominators i.e. for 65,89,839 is 4853615.

Thus, GCF of Fractions is 1/4853615.Finally, GCF of Fractions for 66/65, 204/89, 829/839 is 1/4853615.