How to Find GCF of 85/76, 96/20, 46/204?

GCF of 85/76, 96/20, 46/204

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 85/76, 96/20, 46/204 i.e 1/19380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 85/76, 96/20, 46/204.

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 85/76,96/20,46/204?

Given fractions are 85/76,96/20,46/204

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 85/76,96/20,46/204, numerators are 85,96,46

Denominators are 76,20,204

The GCF of 85,96,46 is 1 .

LCM of 76,20,204 is 19380.

The greatest common factor of 85/76,96/20,46/204 = [GCF of 85,96,46]/[LCM of 76,20,204]= 1/19380

Therefore, the GCF of 85/76,96/20,46/204 is 1/19380.

Greatest Common Factor of 85,96,46

To find the highest common factor of 85,96,46, 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 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

The factors of 46 are 1, 2, 23, 46

The HCF of 85,96,46 is 1.

Lets's calculate GCF of 85,96,46

Greatest Common Factor (GCF) of 85,96,46 By Common Division

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

Greatest Common Factor of 85,96,46 By Matching Biggest Common Factor Method

Now, list down the factors of 85

1,5,17,85

Now, list down the factors of 96

1,2,3,4,6,8,12,16,24,32,48,96

Now, list down the factors of 46

1,2,23,46

Greatest Common Factor

We found the factors 85,96,46 . The biggest common factor number is the GCF number.
So the greatest common factor 85,96,46 is 1.

Lets's calculate LCM of 76,20,204

Lowest Common Multiple of 76,20,204 using Common Division

2	76, 20, 204
2	38, 10, 102
	19, 5, 51

∴ So the LCM of the given numbers is 2 x 2 x 19 x 5 x 51 = 19380

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/19380

Therefore, the GCF of Fractions 85/76,96/20,46/204 is 1/19380

Least Common Multiple of 76,20,204 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 76,20,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,20,204) = 4

common factors(in case of two or more numbers have common factors) = 4

GCF(76,20,204) x common factors =4 x 4 = 16

LCM(76,20,204) = ( 76 × 20 × 204 ) / 16

LCM(76,20,204) = 310080 / 16

LCM(76,20,204) = 19380

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 85/76, 96/20, 46/204

1. What is the HCF of 85,96,46?

The HCF of 85,96,46 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 85/76, 96/20, 46/204?

Answer: GCF of Numerators as per given numbers 85/76, 96/20, 46/204 is

GCF of Numerators i.e. for 85,96,46 is 1

LCM of denominators i.e. for 76,20,204 is 19380.

Thus, GCF of Fractions is 1/19380.Finally, GCF of Fractions for 85/76, 96/20, 46/204 is 1/19380.