How to Find GCF of 85/78, 19/65, 610/780?

GCF of 85/78, 19/65, 610/780

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 85/78, 19/65, 610/780 i.e 1/780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 85/78, 19/65, 610/780.

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 85/78,19/65,610/780?

Given fractions are 85/78,19/65,610/780

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 85/78,19/65,610/780, numerators are 85,19,610

Denominators are 78,65,780

The GCF of 85,19,610 is 1 .

LCM of 78,65,780 is 780.

The greatest common factor of 85/78,19/65,610/780 = [GCF of 85,19,610]/[LCM of 78,65,780]= 1/780

Therefore, the GCF of 85/78,19/65,610/780 is 1/780.

Greatest Common Factor of 85,19,610

To find the highest common factor of 85,19,610, we have to find the factors of both numbers and list the highest common factor.

The factors of 85 are 1, 5, 17, 85

The factors of 19 are 1, 19

The factors of 610 are 1, 2, 5, 10, 61, 122, 305, 610

The HCF of 85,19,610 is 1.

Lets's calculate GCF of 85,19,610

Greatest Common Factor (GCF) of 85,19,610 By Common Division

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

Greatest Common Factor of 85,19,610 By Matching Biggest Common Factor Method

Now, list down the factors of 85

1,5,17,85

Now, list down the factors of 19

1,19

Now, list down the factors of 610

1,2,5,10,61,122,305,610

Greatest Common Factor

We found the factors 85,19,610 . The biggest common factor number is the GCF number.
So the greatest common factor 85,19,610 is 1.

Lets's calculate LCM of 78,65,780

Lowest Common Multiple of 78,65,780 using Common Division

2	78, 65, 780
3	39, 65, 390
5	13, 65, 130
13	13, 13, 26
	1, 1, 2

∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 1 x 1 x 2 = 780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/780

Therefore, the GCF of Fractions 85/78,19/65,610/780 is 1/780

Least Common Multiple of 78,65,780 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 78,65,780 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,65,780) = 13

common factors(in case of two or more numbers have common factors) = 390

GCF(78,65,780) x common factors =13 x 390 = 5070

LCM(78,65,780) = ( 78 × 65 × 780 ) / 5070

LCM(78,65,780) = 3954600 / 5070

LCM(78,65,780) = 780

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 85/78, 19/65, 610/780

1. What is the HCF of 85,19,610?

The HCF of 85,19,610 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 85/78, 19/65, 610/780?

Answer: GCF of Numerators as per given numbers 85/78, 19/65, 610/780 is

GCF of Numerators i.e. for 85,19,610 is 1

LCM of denominators i.e. for 78,65,780 is 780.

Thus, GCF of Fractions is 1/780.Finally, GCF of Fractions for 85/78, 19/65, 610/780 is 1/780.