How to Find GCF of 677/288, 3826/672?

GCF of 677/288, 3826/672

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 677/288, 3826/672 i.e 1/2016 easily. The following is the detailed procedure to determine the greatest common factor of fractions 677/288, 3826/672.

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 677/288,3826/672?

Given fractions are 677/288,3826/672

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 677/288,3826/672, numerators are 677,3826

Denominators are 288,672

The GCF of 677,3826 is 1 .

LCM of 288,672 is 2016.

The greatest common factor of 677/288,3826/672 = [GCF of 677,3826]/[LCM of 288,672]= 1/2016

Therefore, the GCF of 677/288,3826/672 is 1/2016.

Greatest Common Factor of 677,3826

To find the highest common factor of 677,3826, we have to find the factors of both numbers and list the highest common factor.

The factors of 677 are 1, 677

The factors of 3826 are 1, 2, 1913, 3826

The HCF of 677,3826 is 1.

Lets's calculate GCF of 677,3826

Greatest Common Factor (GCF) of 677,3826 By Common Division

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

Greatest Common Factor of 677,3826 By Matching Biggest Common Factor Method

Now, list down the factors of 677

1,677

Now, list down the factors of 3826

1,2,1913,3826

Greatest Common Factor

We found the factors 677,3826 . The biggest common factor number is the GCF number.
So the greatest common factor 677,3826 is 1.

Lets's calculate LCM of 288,672

Lowest Common Multiple of 288,672 using Common Division

2	288, 672
2	144, 336
2	72, 168
2	36, 84
2	18, 42
3	9, 21
	3, 7

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 = 2016

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2016

Therefore, the GCF of Fractions 677/288,3826/672 is 1/2016

Least Common Multiple of 288,672 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 288,672 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(288,672) = 96

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

GCF(288,672) x common factors =96 x 1 = 96

LCM(288,672) = ( 288 × 672 ) / 96

LCM(288,672) = 193536 / 96

LCM(288,672) = 2016

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FAQs on GCF of Fractions of 677/288, 3826/672

1. What is the HCF of 677,3826?

The HCF of 677,3826 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 677/288, 3826/672?

Answer: GCF of Numerators as per given numbers 677/288, 3826/672 is

GCF of Numerators i.e. for 677,3826 is 1

LCM of denominators i.e. for 288,672 is 2016.

Thus, GCF of Fractions is 1/2016.Finally, GCF of Fractions for 677/288, 3826/672 is 1/2016.