How to Find GCF of 41/614, 56/321, 198/700?

GCF of 41/614, 56/321, 198/700

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 41/614, 56/321, 198/700 i.e 1/68982900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 41/614, 56/321, 198/700.

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 41/614,56/321,198/700?

Given fractions are 41/614,56/321,198/700

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 41/614,56/321,198/700, numerators are 41,56,198

Denominators are 614,321,700

The GCF of 41,56,198 is 1 .

LCM of 614,321,700 is 68982900.

The greatest common factor of 41/614,56/321,198/700 = [GCF of 41,56,198]/[LCM of 614,321,700]= 1/68982900

Therefore, the GCF of 41/614,56/321,198/700 is 1/68982900.

Greatest Common Factor of 41,56,198

To find the highest common factor of 41,56,198, we have to find the factors of both numbers and list the highest common factor.

The factors of 41 are 1, 41

The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198

The HCF of 41,56,198 is 1.

Lets's calculate GCF of 41,56,198

Greatest Common Factor (GCF) of 41,56,198 By Common Division

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

Greatest Common Factor of 41,56,198 By Matching Biggest Common Factor Method

Now, list down the factors of 41

1,41

Now, list down the factors of 56

1,2,4,7,8,14,28,56

Now, list down the factors of 198

1,2,3,6,9,11,18,22,33,66,99,198

Greatest Common Factor

We found the factors 41,56,198 . The biggest common factor number is the GCF number.
So the greatest common factor 41,56,198 is 1.

Lets's calculate LCM of 614,321,700

Lowest Common Multiple of 614,321,700 using Common Division

2	614, 321, 700
	307, 321, 350

∴ So the LCM of the given numbers is 2 x 307 x 321 x 350 = 68982900

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/68982900

Therefore, the GCF of Fractions 41/614,56/321,198/700 is 1/68982900

Least Common Multiple of 614,321,700 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 614,321,700 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(614,321,700) = 1

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

GCF(614,321,700) x common factors =1 x 2 = 2

LCM(614,321,700) = ( 614 × 321 × 700 ) / 2

LCM(614,321,700) = 137965800 / 2

LCM(614,321,700) = 68982900

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 41/614, 56/321, 198/700

1. What is the HCF of 41,56,198?

The HCF of 41,56,198 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 41/614, 56/321, 198/700?

Answer: GCF of Numerators as per given numbers 41/614, 56/321, 198/700 is

GCF of Numerators i.e. for 41,56,198 is 1

LCM of denominators i.e. for 614,321,700 is 68982900.

Thus, GCF of Fractions is 1/68982900.Finally, GCF of Fractions for 41/614, 56/321, 198/700 is 1/68982900.