How to Find GCF of 81/42, 71/30, 296/35?

GCF of 81/42, 71/30, 296/35

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 81/42, 71/30, 296/35 i.e 1/210 easily. The following is the detailed procedure to determine the greatest common factor of fractions 81/42, 71/30, 296/35.

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 81/42,71/30,296/35?

Given fractions are 81/42,71/30,296/35

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 81/42,71/30,296/35, numerators are 81,71,296

Denominators are 42,30,35

The GCF of 81,71,296 is 1 .

LCM of 42,30,35 is 210.

The greatest common factor of 81/42,71/30,296/35 = [GCF of 81,71,296]/[LCM of 42,30,35]= 1/210

Therefore, the GCF of 81/42,71/30,296/35 is 1/210.

Greatest Common Factor of 81,71,296

To find the highest common factor of 81,71,296, we have to find the factors of both numbers and list the highest common factor.

The factors of 81 are 1, 3, 9, 27, 81

The factors of 71 are 1, 71

The factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296

The HCF of 81,71,296 is 1.

Lets's calculate GCF of 81,71,296

Greatest Common Factor (GCF) of 81,71,296 By Common Division

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

Greatest Common Factor of 81,71,296 By Matching Biggest Common Factor Method

Now, list down the factors of 81

1,3,9,27,81

Now, list down the factors of 71

1,71

Now, list down the factors of 296

1,2,4,8,37,74,148,296

Greatest Common Factor

We found the factors 81,71,296 . The biggest common factor number is the GCF number.
So the greatest common factor 81,71,296 is 1.

Lets's calculate LCM of 42,30,35

Lowest Common Multiple of 42,30,35 using Common Division

2	42, 30, 35
3	21, 15, 35
5	7, 5, 35
7	7, 1, 7
	1, 1, 1

∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 1 x 1 x 1 = 210

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/210

Therefore, the GCF of Fractions 81/42,71/30,296/35 is 1/210

Least Common Multiple of 42,30,35 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 42,30,35 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,30,35) = 1

common factors(in case of two or more numbers have common factors) = 210

GCF(42,30,35) x common factors =1 x 210 = 210

LCM(42,30,35) = ( 42 × 30 × 35 ) / 210

LCM(42,30,35) = 44100 / 210

LCM(42,30,35) = 210

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 81/42, 71/30, 296/35

1. What is the HCF of 81,71,296?

The HCF of 81,71,296 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 81/42, 71/30, 296/35?

Answer: GCF of Numerators as per given numbers 81/42, 71/30, 296/35 is

GCF of Numerators i.e. for 81,71,296 is 1

LCM of denominators i.e. for 42,30,35 is 210.

Thus, GCF of Fractions is 1/210.Finally, GCF of Fractions for 81/42, 71/30, 296/35 is 1/210.