How to Find GCF of 46/200, 70/984, 218/428?

GCF of 46/200, 70/984, 218/428

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 46/200, 70/984, 218/428 i.e 2/2632200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 46/200, 70/984, 218/428.

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 46/200,70/984,218/428?

Given fractions are 46/200,70/984,218/428

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 46/200,70/984,218/428, numerators are 46,70,218

Denominators are 200,984,428

The GCF of 46,70,218 is 2 .

LCM of 200,984,428 is 2632200.

The greatest common factor of 46/200,70/984,218/428 = [GCF of 46,70,218]/[LCM of 200,984,428]= 2/2632200

Therefore, the GCF of 46/200,70/984,218/428 is 2/2632200.

Greatest Common Factor of 46,70,218

To find the highest common factor of 46,70,218, we have to find the factors of both numbers and list the highest common factor.

The factors of 46 are 1, 2, 23, 46

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70

The factors of 218 are 1, 2, 109, 218

The HCF of 46,70,218 is 2.

Lets's calculate GCF of 46,70,218

Greatest Common Factor (GCF) of 46,70,218 By Common Division

2	46, 70, 218
	23, 35, 109

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 46,70,218 By Matching Biggest Common Factor Method

Now, list down the factors of 46

1,2,23,46

Now, list down the factors of 70

1,2,5,7,10,14,35,70

Now, list down the factors of 218

1,2,109,218

Greatest Common Factor

We found the factors 46,70,218 . The biggest common factor number is the GCF number.
So the greatest common factor 46,70,218 is 2.

Lets's calculate LCM of 200,984,428

Lowest Common Multiple of 200,984,428 using Common Division

2	200, 984, 428
2	100, 492, 214
2	50, 246, 107
	25, 123, 107

∴ So the LCM of the given numbers is 2 x 2 x 2 x 25 x 123 x 107 = 2632200

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2632200

Therefore, the GCF of Fractions 46/200,70/984,218/428 is 2/2632200

Least Common Multiple of 200,984,428 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 200,984,428 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(200,984,428) = 4

common factors(in case of two or more numbers have common factors) = 8

GCF(200,984,428) x common factors =4 x 8 = 32

LCM(200,984,428) = ( 200 × 984 × 428 ) / 32

LCM(200,984,428) = 84230400 / 32

LCM(200,984,428) = 2632200

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 46/200, 70/984, 218/428

1. What is the HCF of 46,70,218?

The HCF of 46,70,218 is 2

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 46/200, 70/984, 218/428?

Answer: GCF of Numerators as per given numbers 46/200, 70/984, 218/428 is

GCF of Numerators i.e. for 46,70,218 is 2

LCM of denominators i.e. for 200,984,428 is 2632200.

Thus, GCF of Fractions is 2/2632200.Finally, GCF of Fractions for 46/200, 70/984, 218/428 is 2/2632200.