How to Find GCF of 8469/289, 8974/4228?

GCF of 8469/289, 8974/4228

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 8469/289, 8974/4228 i.e 1/1221892 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8469/289, 8974/4228.

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 8469/289,8974/4228?

Given fractions are 8469/289,8974/4228

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 8469/289,8974/4228, numerators are 8469,8974

Denominators are 289,4228

The GCF of 8469,8974 is 1 .

LCM of 289,4228 is 1221892.

The greatest common factor of 8469/289,8974/4228 = [GCF of 8469,8974]/[LCM of 289,4228]= 1/1221892

Therefore, the GCF of 8469/289,8974/4228 is 1/1221892.

Greatest Common Factor of 8469,8974

To find the highest common factor of 8469,8974, we have to find the factors of both numbers and list the highest common factor.

The factors of 8469 are 1, 3, 9, 941, 2823, 8469

The factors of 8974 are 1, 2, 7, 14, 641, 1282, 4487, 8974

The HCF of 8469,8974 is 1.

Lets's calculate GCF of 8469,8974

Greatest Common Factor (GCF) of 8469,8974 By Common Division

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

Greatest Common Factor of 8469,8974 By Matching Biggest Common Factor Method

Now, list down the factors of 8469

1,3,9,941,2823,8469

Now, list down the factors of 8974

1,2,7,14,641,1282,4487,8974

Greatest Common Factor

We found the factors 8469,8974 . The biggest common factor number is the GCF number.
So the greatest common factor 8469,8974 is 1.

Lets's calculate LCM of 289,4228

Lowest Common Multiple of 289,4228 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1221892

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1221892

Therefore, the GCF of Fractions 8469/289,8974/4228 is 1/1221892

Least Common Multiple of 289,4228 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 289,4228 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,4228) = 1

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

GCF(289,4228) x common factors =1 x 1 = 1

LCM(289,4228) = ( 289 × 4228 ) / 1

LCM(289,4228) = 1221892 / 1

LCM(289,4228) = 1221892

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FAQs on GCF of Fractions of 8469/289, 8974/4228

1. What is the HCF of 8469,8974?

The HCF of 8469,8974 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 8469/289, 8974/4228?

Answer: GCF of Numerators as per given numbers 8469/289, 8974/4228 is

GCF of Numerators i.e. for 8469,8974 is 1

LCM of denominators i.e. for 289,4228 is 1221892.

Thus, GCF of Fractions is 1/1221892.Finally, GCF of Fractions for 8469/289, 8974/4228 is 1/1221892.