How to Find GCF of 8431/684, 1470/234?

GCF of 8431/684, 1470/234

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 8431/684, 1470/234 i.e 1/8892 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8431/684, 1470/234.

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 8431/684,1470/234?

Given fractions are 8431/684,1470/234

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 8431/684,1470/234, numerators are 8431,1470

Denominators are 684,234

The GCF of 8431,1470 is 1 .

LCM of 684,234 is 8892.

The greatest common factor of 8431/684,1470/234 = [GCF of 8431,1470]/[LCM of 684,234]= 1/8892

Therefore, the GCF of 8431/684,1470/234 is 1/8892.

Greatest Common Factor of 8431,1470

To find the highest common factor of 8431,1470, we have to find the factors of both numbers and list the highest common factor.

The factors of 8431 are 1, 8431

The factors of 1470 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470

The HCF of 8431,1470 is 1.

Lets's calculate GCF of 8431,1470

Greatest Common Factor (GCF) of 8431,1470 By Common Division

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

Greatest Common Factor of 8431,1470 By Matching Biggest Common Factor Method

Now, list down the factors of 8431

1,8431

Now, list down the factors of 1470

1,2,3,5,6,7,10,14,15,21,30,35,42,49,70,98,105,147,210,245,294,490,735,1470

Greatest Common Factor

We found the factors 8431,1470 . The biggest common factor number is the GCF number.
So the greatest common factor 8431,1470 is 1.

Lets's calculate LCM of 684,234

Lowest Common Multiple of 684,234 using Common Division

2	684, 234
3	342, 117
3	114, 39
	38, 13

∴ So the LCM of the given numbers is 2 x 3 x 3 x 38 x 13 = 8892

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8892

Therefore, the GCF of Fractions 8431/684,1470/234 is 1/8892

Least Common Multiple of 684,234 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 684,234 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(684,234) = 18

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

GCF(684,234) x common factors =18 x 1 = 18

LCM(684,234) = ( 684 × 234 ) / 18

LCM(684,234) = 160056 / 18

LCM(684,234) = 8892

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FAQs on GCF of Fractions of 8431/684, 1470/234

1. What is the HCF of 8431,1470?

The HCF of 8431,1470 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 8431/684, 1470/234?

Answer: GCF of Numerators as per given numbers 8431/684, 1470/234 is

GCF of Numerators i.e. for 8431,1470 is 1

LCM of denominators i.e. for 684,234 is 8892.

Thus, GCF of Fractions is 1/8892.Finally, GCF of Fractions for 8431/684, 1470/234 is 1/8892.