How to Find GCF of 831/865, 784/419?

GCF of 831/865, 784/419

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 831/865, 784/419 i.e 1/362435 easily. The following is the detailed procedure to determine the greatest common factor of fractions 831/865, 784/419.

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 831/865,784/419?

Given fractions are 831/865,784/419

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 831/865,784/419, numerators are 831,784

Denominators are 865,419

The GCF of 831,784 is 1 .

LCM of 865,419 is 362435.

The greatest common factor of 831/865,784/419 = [GCF of 831,784]/[LCM of 865,419]= 1/362435

Therefore, the GCF of 831/865,784/419 is 1/362435.

Greatest Common Factor of 831,784

To find the highest common factor of 831,784, we have to find the factors of both numbers and list the highest common factor.

The factors of 831 are 1, 3, 277, 831

The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784

The HCF of 831,784 is 1.

Lets's calculate GCF of 831,784

Greatest Common Factor (GCF) of 831,784 By Common Division

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

Greatest Common Factor of 831,784 By Matching Biggest Common Factor Method

Now, list down the factors of 831

1,3,277,831

Now, list down the factors of 784

1,2,4,7,8,14,16,28,49,56,98,112,196,392,784

Greatest Common Factor

We found the factors 831,784 . The biggest common factor number is the GCF number.
So the greatest common factor 831,784 is 1.

Lets's calculate LCM of 865,419

Lowest Common Multiple of 865,419 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 362435

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/362435

Therefore, the GCF of Fractions 831/865,784/419 is 1/362435

Least Common Multiple of 865,419 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 865,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(865,419) = 1

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

GCF(865,419) x common factors =1 x 1 = 1

LCM(865,419) = ( 865 × 419 ) / 1

LCM(865,419) = 362435 / 1

LCM(865,419) = 362435

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FAQs on GCF of Fractions of 831/865, 784/419

1. What is the HCF of 831,784?

The HCF of 831,784 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 831/865, 784/419?

Answer: GCF of Numerators as per given numbers 831/865, 784/419 is

GCF of Numerators i.e. for 831,784 is 1

LCM of denominators i.e. for 865,419 is 362435.

Thus, GCF of Fractions is 1/362435.Finally, GCF of Fractions for 831/865, 784/419 is 1/362435.