How to Find GCF of 783/176, 3825/544?

GCF of 783/176, 3825/544

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 783/176, 3825/544 i.e 9/5984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 783/176, 3825/544.

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 783/176,3825/544?

Given fractions are 783/176,3825/544

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 783/176,3825/544, numerators are 783,3825

Denominators are 176,544

The GCF of 783,3825 is 9 .

LCM of 176,544 is 5984.

The greatest common factor of 783/176,3825/544 = [GCF of 783,3825]/[LCM of 176,544]= 9/5984

Therefore, the GCF of 783/176,3825/544 is 9/5984.

Greatest Common Factor of 783,3825

To find the highest common factor of 783,3825, we have to find the factors of both numbers and list the highest common factor.

The factors of 783 are 1, 3, 9, 27, 29, 87, 261, 783

The factors of 3825 are 1, 3, 5, 9, 15, 17, 25, 45, 51, 75, 85, 153, 225, 255, 425, 765, 1275, 3825

The HCF of 783,3825 is 9.

Lets's calculate GCF of 783,3825

Greatest Common Factor (GCF) of 783,3825 By Common Division

3	783, 3825
3	261, 1275
	87, 425

∴ So the GCF of the given numbers is 3 x 3 = 9

Greatest Common Factor of 783,3825 By Matching Biggest Common Factor Method

Now, list down the factors of 783

1,3,9,27,29,87,261,783

Now, list down the factors of 3825

1,3,5,9,15,17,25,45,51,75,85,153,225,255,425,765,1275,3825

Greatest Common Factor

We found the factors 783,3825 . The biggest common factor number is the GCF number.
So the greatest common factor 783,3825 is 9.

Lets's calculate LCM of 176,544

Lowest Common Multiple of 176,544 using Common Division

2	176, 544
2	88, 272
2	44, 136
2	22, 68
	11, 34

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 11 x 34 = 5984

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/5984

Therefore, the GCF of Fractions 783/176,3825/544 is 9/5984

Least Common Multiple of 176,544 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 176,544 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(176,544) = 16

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

GCF(176,544) x common factors =16 x 1 = 16

LCM(176,544) = ( 176 × 544 ) / 16

LCM(176,544) = 95744 / 16

LCM(176,544) = 5984

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FAQs on GCF of Fractions of 783/176, 3825/544

1. What is the HCF of 783,3825?

The HCF of 783,3825 is 9

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 783/176, 3825/544?

Answer: GCF of Numerators as per given numbers 783/176, 3825/544 is

GCF of Numerators i.e. for 783,3825 is 9

LCM of denominators i.e. for 176,544 is 5984.

Thus, GCF of Fractions is 9/5984.Finally, GCF of Fractions for 783/176, 3825/544 is 9/5984.