How to Find GCF of 8314/914, 8230/1005?

GCF of 8314/914, 8230/1005

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 8314/914, 8230/1005 i.e 2/918570 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8314/914, 8230/1005.

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 8314/914,8230/1005?

Given fractions are 8314/914,8230/1005

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 8314/914,8230/1005, numerators are 8314,8230

Denominators are 914,1005

The GCF of 8314,8230 is 2 .

LCM of 914,1005 is 918570.

The greatest common factor of 8314/914,8230/1005 = [GCF of 8314,8230]/[LCM of 914,1005]= 2/918570

Therefore, the GCF of 8314/914,8230/1005 is 2/918570.

Greatest Common Factor of 8314,8230

To find the highest common factor of 8314,8230, we have to find the factors of both numbers and list the highest common factor.

The factors of 8314 are 1, 2, 4157, 8314

The factors of 8230 are 1, 2, 5, 10, 823, 1646, 4115, 8230

The HCF of 8314,8230 is 2.

Lets's calculate GCF of 8314,8230

Greatest Common Factor (GCF) of 8314,8230 By Common Division

2	8314, 8230
	4157, 4115

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 8314,8230 By Matching Biggest Common Factor Method

Now, list down the factors of 8314

1,2,4157,8314

Now, list down the factors of 8230

1,2,5,10,823,1646,4115,8230

Greatest Common Factor

We found the factors 8314,8230 . The biggest common factor number is the GCF number.
So the greatest common factor 8314,8230 is 2.

Lets's calculate LCM of 914,1005

Lowest Common Multiple of 914,1005 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 918570

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/918570

Therefore, the GCF of Fractions 8314/914,8230/1005 is 2/918570

Least Common Multiple of 914,1005 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 914,1005 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(914,1005) = 1

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

GCF(914,1005) x common factors =1 x 1 = 1

LCM(914,1005) = ( 914 × 1005 ) / 1

LCM(914,1005) = 918570 / 1

LCM(914,1005) = 918570

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FAQs on GCF of Fractions of 8314/914, 8230/1005

1. What is the HCF of 8314,8230?

The HCF of 8314,8230 is 2

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 8314/914, 8230/1005?

Answer: GCF of Numerators as per given numbers 8314/914, 8230/1005 is

GCF of Numerators i.e. for 8314,8230 is 2

LCM of denominators i.e. for 914,1005 is 918570.

Thus, GCF of Fractions is 2/918570.Finally, GCF of Fractions for 8314/914, 8230/1005 is 2/918570.