How to Find GCF of 43/14, 82/50, 429/762?

GCF of 43/14, 82/50, 429/762

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 43/14, 82/50, 429/762 i.e 1/133350 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/14, 82/50, 429/762.

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 43/14,82/50,429/762?

Given fractions are 43/14,82/50,429/762

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 43/14,82/50,429/762, numerators are 43,82,429

Denominators are 14,50,762

The GCF of 43,82,429 is 1 .

LCM of 14,50,762 is 133350.

The greatest common factor of 43/14,82/50,429/762 = [GCF of 43,82,429]/[LCM of 14,50,762]= 1/133350

Therefore, the GCF of 43/14,82/50,429/762 is 1/133350.

Greatest Common Factor of 43,82,429

To find the highest common factor of 43,82,429, 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 82 are 1, 2, 41, 82

The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429

The HCF of 43,82,429 is 1.

Lets's calculate GCF of 43,82,429

Greatest Common Factor (GCF) of 43,82,429 By Common Division

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

Greatest Common Factor of 43,82,429 By Matching Biggest Common Factor Method

Now, list down the factors of 43

1,43

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 429

1,3,11,13,33,39,143,429

Greatest Common Factor

We found the factors 43,82,429 . The biggest common factor number is the GCF number.
So the greatest common factor 43,82,429 is 1.

Lets's calculate LCM of 14,50,762

Lowest Common Multiple of 14,50,762 using Common Division

2	14, 50, 762
	7, 25, 381

∴ So the LCM of the given numbers is 2 x 7 x 25 x 381 = 133350

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/133350

Therefore, the GCF of Fractions 43/14,82/50,429/762 is 1/133350

Least Common Multiple of 14,50,762 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 14,50,762 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,50,762) = 2

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

GCF(14,50,762) x common factors =2 x 2 = 4

LCM(14,50,762) = ( 14 × 50 × 762 ) / 4

LCM(14,50,762) = 533400 / 4

LCM(14,50,762) = 133350

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FAQs on GCF of Fractions of 43/14, 82/50, 429/762

1. What is the HCF of 43,82,429?

The HCF of 43,82,429 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 43/14, 82/50, 429/762?

Answer: GCF of Numerators as per given numbers 43/14, 82/50, 429/762 is

GCF of Numerators i.e. for 43,82,429 is 1

LCM of denominators i.e. for 14,50,762 is 133350.

Thus, GCF of Fractions is 1/133350.Finally, GCF of Fractions for 43/14, 82/50, 429/762 is 1/133350.