How to Find GCF of 43/16, 61/84, 438/76?

GCF of 43/16, 61/84, 438/76

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 43/16, 61/84, 438/76 i.e 1/6384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/16, 61/84, 438/76.

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 43/16,61/84,438/76?

Given fractions are 43/16,61/84,438/76

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 43/16,61/84,438/76, numerators are 43,61,438

Denominators are 16,84,76

The GCF of 43,61,438 is 1 .

LCM of 16,84,76 is 6384.

The greatest common factor of 43/16,61/84,438/76 = [GCF of 43,61,438]/[LCM of 16,84,76]= 1/6384

Therefore, the GCF of 43/16,61/84,438/76 is 1/6384.

Greatest Common Factor of 43,61,438

To find the highest common factor of 43,61,438, 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 61 are 1, 61

The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438

The HCF of 43,61,438 is 1.

Lets's calculate GCF of 43,61,438

Greatest Common Factor (GCF) of 43,61,438 By Common Division

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

Greatest Common Factor of 43,61,438 By Matching Biggest Common Factor Method

Now, list down the factors of 43

1,43

Now, list down the factors of 61

1,61

Now, list down the factors of 438

1,2,3,6,73,146,219,438

Greatest Common Factor

We found the factors 43,61,438 . The biggest common factor number is the GCF number.
So the greatest common factor 43,61,438 is 1.

Lets's calculate LCM of 16,84,76

Lowest Common Multiple of 16,84,76 using Common Division

2	16, 84, 76
2	8, 42, 38
	4, 21, 19

∴ So the LCM of the given numbers is 2 x 2 x 4 x 21 x 19 = 6384

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6384

Therefore, the GCF of Fractions 43/16,61/84,438/76 is 1/6384

Least Common Multiple of 16,84,76 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 16,84,76 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,84,76) = 4

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

GCF(16,84,76) x common factors =4 x 4 = 16

LCM(16,84,76) = ( 16 × 84 × 76 ) / 16

LCM(16,84,76) = 102144 / 16

LCM(16,84,76) = 6384

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FAQs on GCF of Fractions of 43/16, 61/84, 438/76

1. What is the HCF of 43,61,438?

The HCF of 43,61,438 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 43/16, 61/84, 438/76?

Answer: GCF of Numerators as per given numbers 43/16, 61/84, 438/76 is

GCF of Numerators i.e. for 43,61,438 is 1

LCM of denominators i.e. for 16,84,76 is 6384.

Thus, GCF of Fractions is 1/6384.Finally, GCF of Fractions for 43/16, 61/84, 438/76 is 1/6384.