How to Find GCF of 43/12, 141/76, 165/874?

GCF of 43/12, 141/76, 165/874

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 43/12, 141/76, 165/874 i.e 1/5244 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/12, 141/76, 165/874.

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 43/12,141/76,165/874?

Given fractions are 43/12,141/76,165/874

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 43/12,141/76,165/874, numerators are 43,141,165

Denominators are 12,76,874

The GCF of 43,141,165 is 1 .

LCM of 12,76,874 is 5244.

The greatest common factor of 43/12,141/76,165/874 = [GCF of 43,141,165]/[LCM of 12,76,874]= 1/5244

Therefore, the GCF of 43/12,141/76,165/874 is 1/5244.

Greatest Common Factor of 43,141,165

To find the highest common factor of 43,141,165, we have to find the factors of both numbers and list the highest common factor.

The factors of 43 are 1, 43

The factors of 141 are 1, 3, 47, 141

The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165

The HCF of 43,141,165 is 1.

Lets's calculate GCF of 43,141,165

Greatest Common Factor (GCF) of 43,141,165 By Common Division

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

Greatest Common Factor of 43,141,165 By Matching Biggest Common Factor Method

Now, list down the factors of 43

1,43

Now, list down the factors of 141

1,3,47,141

Now, list down the factors of 165

1,3,5,11,15,33,55,165

Greatest Common Factor

We found the factors 43,141,165 . The biggest common factor number is the GCF number.
So the greatest common factor 43,141,165 is 1.

Lets's calculate LCM of 12,76,874

Lowest Common Multiple of 12,76,874 using Common Division

2	12, 76, 874
2	6, 38, 437
19	3, 19, 437
	3, 1, 23

∴ So the LCM of the given numbers is 2 x 2 x 19 x 3 x 1 x 23 = 5244

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5244

Therefore, the GCF of Fractions 43/12,141/76,165/874 is 1/5244

Least Common Multiple of 12,76,874 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 12,76,874 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,76,874) = 2

common factors(in case of two or more numbers have common factors) = 76

GCF(12,76,874) x common factors =2 x 76 = 152

LCM(12,76,874) = ( 12 × 76 × 874 ) / 152

LCM(12,76,874) = 797088 / 152

LCM(12,76,874) = 5244

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FAQs on GCF of Fractions of 43/12, 141/76, 165/874

1. What is the HCF of 43,141,165?

The HCF of 43,141,165 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 43/12, 141/76, 165/874?

Answer: GCF of Numerators as per given numbers 43/12, 141/76, 165/874 is

GCF of Numerators i.e. for 43,141,165 is 1

LCM of denominators i.e. for 12,76,874 is 5244.

Thus, GCF of Fractions is 1/5244.Finally, GCF of Fractions for 43/12, 141/76, 165/874 is 1/5244.