How to Find GCF of 660/783, 406/774?

GCF of 660/783, 406/774

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 660/783, 406/774 i.e 2/67338 easily. The following is the detailed procedure to determine the greatest common factor of fractions 660/783, 406/774.

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 660/783,406/774?

Given fractions are 660/783,406/774

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 660/783,406/774, numerators are 660,406

Denominators are 783,774

The GCF of 660,406 is 2 .

LCM of 783,774 is 67338.

The greatest common factor of 660/783,406/774 = [GCF of 660,406]/[LCM of 783,774]= 2/67338

Therefore, the GCF of 660/783,406/774 is 2/67338.

Greatest Common Factor of 660,406

To find the highest common factor of 660,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 660,406 is 2.

Lets's calculate GCF of 660,406

Greatest Common Factor (GCF) of 660,406 By Common Division

2	660, 406
	330, 203

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

Greatest Common Factor of 660,406 By Matching Biggest Common Factor Method

Now, list down the factors of 660

1,2,3,4,5,6,10,11,12,15,20,22,30,33,44,55,60,66,110,132,165,220,330,660

Now, list down the factors of 406

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 660,406 . The biggest common factor number is the GCF number.
So the greatest common factor 660,406 is 2.

Lets's calculate LCM of 783,774

Lowest Common Multiple of 783,774 using Common Division

3	783, 774
3	261, 258
	87, 86

∴ So the LCM of the given numbers is 3 x 3 x 87 x 86 = 67338

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/67338

Therefore, the GCF of Fractions 660/783,406/774 is 2/67338

Least Common Multiple of 783,774 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 783,774 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(783,774) = 9

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

GCF(783,774) x common factors =9 x 1 = 9

LCM(783,774) = ( 783 × 774 ) / 9

LCM(783,774) = 606042 / 9

LCM(783,774) = 67338

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FAQs on GCF of Fractions of 660/783, 406/774

1. What is the HCF of 660,406?

The HCF of 660,406 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 660/783, 406/774?

Answer: GCF of Numerators as per given numbers 660/783, 406/774 is

GCF of Numerators i.e. for 660,406 is 2

LCM of denominators i.e. for 783,774 is 67338.

Thus, GCF of Fractions is 2/67338.Finally, GCF of Fractions for 660/783, 406/774 is 2/67338.