How to Find GCF of 44/74, 10/14, 499/421?

GCF of 44/74, 10/14, 499/421

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 44/74, 10/14, 499/421 i.e 1/218078 easily. The following is the detailed procedure to determine the greatest common factor of fractions 44/74, 10/14, 499/421.

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 44/74,10/14,499/421?

Given fractions are 44/74,10/14,499/421

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 44/74,10/14,499/421, numerators are 44,10,499

Denominators are 74,14,421

The GCF of 44,10,499 is 1 .

LCM of 74,14,421 is 218078.

The greatest common factor of 44/74,10/14,499/421 = [GCF of 44,10,499]/[LCM of 74,14,421]= 1/218078

Therefore, the GCF of 44/74,10/14,499/421 is 1/218078.

Greatest Common Factor of 44,10,499

To find the highest common factor of 44,10,499, we have to find the factors of both numbers and list the highest common factor.

The factors of 44 are 1, 2, 4, 11, 22, 44

The factors of 10 are 1, 2, 5, 10

The factors of 499 are 1, 499

The HCF of 44,10,499 is 1.

Lets's calculate GCF of 44,10,499

Greatest Common Factor (GCF) of 44,10,499 By Common Division

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

Greatest Common Factor of 44,10,499 By Matching Biggest Common Factor Method

Now, list down the factors of 44

1,2,4,11,22,44

Now, list down the factors of 10

1,2,5,10

Now, list down the factors of 499

1,499

Greatest Common Factor

We found the factors 44,10,499 . The biggest common factor number is the GCF number.
So the greatest common factor 44,10,499 is 1.

Lets's calculate LCM of 74,14,421

Lowest Common Multiple of 74,14,421 using Common Division

2	74, 14, 421
	37, 7, 421

∴ So the LCM of the given numbers is 2 x 37 x 7 x 421 = 218078

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/218078

Therefore, the GCF of Fractions 44/74,10/14,499/421 is 1/218078

Least Common Multiple of 74,14,421 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 74,14,421 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(74,14,421) = 1

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

GCF(74,14,421) x common factors =1 x 2 = 2

LCM(74,14,421) = ( 74 × 14 × 421 ) / 2

LCM(74,14,421) = 436156 / 2

LCM(74,14,421) = 218078

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FAQs on GCF of Fractions of 44/74, 10/14, 499/421

1. What is the HCF of 44,10,499?

The HCF of 44,10,499 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 44/74, 10/14, 499/421?

Answer: GCF of Numerators as per given numbers 44/74, 10/14, 499/421 is

GCF of Numerators i.e. for 44,10,499 is 1

LCM of denominators i.e. for 74,14,421 is 218078.

Thus, GCF of Fractions is 1/218078.Finally, GCF of Fractions for 44/74, 10/14, 499/421 is 1/218078.