How to Find GCF of 678/800, 8469/936?

GCF of 678/800, 8469/936

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 678/800, 8469/936 i.e 3/93600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/800, 8469/936.

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 678/800,8469/936?

Given fractions are 678/800,8469/936

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 678/800,8469/936, numerators are 678,8469

Denominators are 800,936

The GCF of 678,8469 is 3 .

LCM of 800,936 is 93600.

The greatest common factor of 678/800,8469/936 = [GCF of 678,8469]/[LCM of 800,936]= 3/93600

Therefore, the GCF of 678/800,8469/936 is 3/93600.

Greatest Common Factor of 678,8469

To find the highest common factor of 678,8469, we have to find the factors of both numbers and list the highest common factor.

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

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

The HCF of 678,8469 is 3.

Lets's calculate GCF of 678,8469

Greatest Common Factor (GCF) of 678,8469 By Common Division

3	678, 8469
	226, 2823

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 678,8469 By Matching Biggest Common Factor Method

Now, list down the factors of 678

1,2,3,6,113,226,339,678

Now, list down the factors of 8469

1,3,9,941,2823,8469

Greatest Common Factor

We found the factors 678,8469 . The biggest common factor number is the GCF number.
So the greatest common factor 678,8469 is 3.

Lets's calculate LCM of 800,936

Lowest Common Multiple of 800,936 using Common Division

2	800, 936
2	400, 468
2	200, 234
	100, 117

∴ So the LCM of the given numbers is 2 x 2 x 2 x 100 x 117 = 93600

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/93600

Therefore, the GCF of Fractions 678/800,8469/936 is 3/93600

Least Common Multiple of 800,936 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 800,936 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(800,936) = 8

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

GCF(800,936) x common factors =8 x 1 = 8

LCM(800,936) = ( 800 × 936 ) / 8

LCM(800,936) = 748800 / 8

LCM(800,936) = 93600

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FAQs on GCF of Fractions of 678/800, 8469/936

1. What is the HCF of 678,8469?

The HCF of 678,8469 is 3

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 678/800, 8469/936?

Answer: GCF of Numerators as per given numbers 678/800, 8469/936 is

GCF of Numerators i.e. for 678,8469 is 3

LCM of denominators i.e. for 800,936 is 93600.

Thus, GCF of Fractions is 3/93600.Finally, GCF of Fractions for 678/800, 8469/936 is 3/93600.