How to Find GCF of 32/49, 85/86, 30/142?

GCF of 32/49, 85/86, 30/142

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 32/49, 85/86, 30/142 i.e 1/299194 easily. The following is the detailed procedure to determine the greatest common factor of fractions 32/49, 85/86, 30/142.

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 32/49,85/86,30/142?

Given fractions are 32/49,85/86,30/142

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 32/49,85/86,30/142, numerators are 32,85,30

Denominators are 49,86,142

The GCF of 32,85,30 is 1 .

LCM of 49,86,142 is 299194.

The greatest common factor of 32/49,85/86,30/142 = [GCF of 32,85,30]/[LCM of 49,86,142]= 1/299194

Therefore, the GCF of 32/49,85/86,30/142 is 1/299194.

Greatest Common Factor of 32,85,30

To find the highest common factor of 32,85,30, we have to find the factors of both numbers and list the highest common factor.

The factors of 32 are 1, 2, 4, 8, 16, 32

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

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The HCF of 32,85,30 is 1.

Lets's calculate GCF of 32,85,30

Greatest Common Factor (GCF) of 32,85,30 By Common Division

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

Greatest Common Factor of 32,85,30 By Matching Biggest Common Factor Method

Now, list down the factors of 32

1,2,4,8,16,32

Now, list down the factors of 85

1,5,17,85

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Greatest Common Factor

We found the factors 32,85,30 . The biggest common factor number is the GCF number.
So the greatest common factor 32,85,30 is 1.

Lets's calculate LCM of 49,86,142

Lowest Common Multiple of 49,86,142 using Common Division

2	49, 86, 142
	49, 43, 71

∴ So the LCM of the given numbers is 2 x 49 x 43 x 71 = 299194

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/299194

Therefore, the GCF of Fractions 32/49,85/86,30/142 is 1/299194

Least Common Multiple of 49,86,142 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 49,86,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(49,86,142) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(49,86,142) x common factors =1 x 2 = 2

LCM(49,86,142) = ( 49 × 86 × 142 ) / 2

LCM(49,86,142) = 598388 / 2

LCM(49,86,142) = 299194

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FAQs on GCF of Fractions of 32/49, 85/86, 30/142

1. What is the HCF of 32,85,30?

The HCF of 32,85,30 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 32/49, 85/86, 30/142?

Answer: GCF of Numerators as per given numbers 32/49, 85/86, 30/142 is

GCF of Numerators i.e. for 32,85,30 is 1

LCM of denominators i.e. for 49,86,142 is 299194.

Thus, GCF of Fractions is 1/299194.Finally, GCF of Fractions for 32/49, 85/86, 30/142 is 1/299194.