How to Find GCF of 86/42, 25/30, 78/20?

GCF of 86/42, 25/30, 78/20

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 86/42, 25/30, 78/20 i.e 1/420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 86/42, 25/30, 78/20.

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 86/42,25/30,78/20?

Given fractions are 86/42,25/30,78/20

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 86/42,25/30,78/20, numerators are 86,25,78

Denominators are 42,30,20

The GCF of 86,25,78 is 1 .

LCM of 42,30,20 is 420.

The greatest common factor of 86/42,25/30,78/20 = [GCF of 86,25,78]/[LCM of 42,30,20]= 1/420

Therefore, the GCF of 86/42,25/30,78/20 is 1/420.

Greatest Common Factor of 86,25,78

To find the highest common factor of 86,25,78, we have to find the factors of both numbers and list the highest common factor.

The factors of 86 are 1, 2, 43, 86

The factors of 25 are 1, 5, 25

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78

The HCF of 86,25,78 is 1.

Lets's calculate GCF of 86,25,78

Greatest Common Factor (GCF) of 86,25,78 By Common Division

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

Greatest Common Factor of 86,25,78 By Matching Biggest Common Factor Method

Now, list down the factors of 86

1,2,43,86

Now, list down the factors of 25

1,5,25

Now, list down the factors of 78

1,2,3,6,13,26,39,78

Greatest Common Factor

We found the factors 86,25,78 . The biggest common factor number is the GCF number.
So the greatest common factor 86,25,78 is 1.

Lets's calculate LCM of 42,30,20

Lowest Common Multiple of 42,30,20 using Common Division

2	42, 30, 20
3	21, 15, 10
5	7, 5, 10
	7, 1, 2

∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 1 x 2 = 420

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/420

Therefore, the GCF of Fractions 86/42,25/30,78/20 is 1/420

Least Common Multiple of 42,30,20 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 42,30,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,30,20) = 2

common factors(in case of two or more numbers have common factors) = 30

GCF(42,30,20) x common factors =2 x 30 = 60

LCM(42,30,20) = ( 42 × 30 × 20 ) / 60

LCM(42,30,20) = 25200 / 60

LCM(42,30,20) = 420

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 86/42, 25/30, 78/20

1. What is the HCF of 86,25,78?

The HCF of 86,25,78 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 86/42, 25/30, 78/20?

Answer: GCF of Numerators as per given numbers 86/42, 25/30, 78/20 is

GCF of Numerators i.e. for 86,25,78 is 1

LCM of denominators i.e. for 42,30,20 is 420.

Thus, GCF of Fractions is 1/420.Finally, GCF of Fractions for 86/42, 25/30, 78/20 is 1/420.