How to Find GCF of 70/19, 83/118, 470/218?

GCF of 70/19, 83/118, 470/218

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 70/19, 83/118, 470/218 i.e 1/244378 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/19, 83/118, 470/218.

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 70/19,83/118,470/218?

Given fractions are 70/19,83/118,470/218

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 70/19,83/118,470/218, numerators are 70,83,470

Denominators are 19,118,218

The GCF of 70,83,470 is 1 .

LCM of 19,118,218 is 244378.

The greatest common factor of 70/19,83/118,470/218 = [GCF of 70,83,470]/[LCM of 19,118,218]= 1/244378

Therefore, the GCF of 70/19,83/118,470/218 is 1/244378.

Greatest Common Factor of 70,83,470

To find the highest common factor of 70,83,470, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 83 are 1, 83

The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470

The HCF of 70,83,470 is 1.

Lets's calculate GCF of 70,83,470

Greatest Common Factor (GCF) of 70,83,470 By Common Division

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

Greatest Common Factor of 70,83,470 By Matching Biggest Common Factor Method

Now, list down the factors of 70

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

Now, list down the factors of 83

1,83

Now, list down the factors of 470

1,2,5,10,47,94,235,470

Greatest Common Factor

We found the factors 70,83,470 . The biggest common factor number is the GCF number.
So the greatest common factor 70,83,470 is 1.

Lets's calculate LCM of 19,118,218

Lowest Common Multiple of 19,118,218 using Common Division

2	19, 118, 218
	19, 59, 109

∴ So the LCM of the given numbers is 2 x 19 x 59 x 109 = 244378

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/244378

Therefore, the GCF of Fractions 70/19,83/118,470/218 is 1/244378

Least Common Multiple of 19,118,218 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 19,118,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(19,118,218) = 1

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

GCF(19,118,218) x common factors =1 x 2 = 2

LCM(19,118,218) = ( 19 × 118 × 218 ) / 2

LCM(19,118,218) = 488756 / 2

LCM(19,118,218) = 244378

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FAQs on GCF of Fractions of 70/19, 83/118, 470/218

1. What is the HCF of 70,83,470?

The HCF of 70,83,470 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 70/19, 83/118, 470/218?

Answer: GCF of Numerators as per given numbers 70/19, 83/118, 470/218 is

GCF of Numerators i.e. for 70,83,470 is 1

LCM of denominators i.e. for 19,118,218 is 244378.

Thus, GCF of Fractions is 1/244378.Finally, GCF of Fractions for 70/19, 83/118, 470/218 is 1/244378.