How to Find GCF of 10/98, 13/70, 824/270?

GCF of 10/98, 13/70, 824/270

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 10/98, 13/70, 824/270 i.e 1/13230 easily. The following is the detailed procedure to determine the greatest common factor of fractions 10/98, 13/70, 824/270.

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 10/98,13/70,824/270?

Given fractions are 10/98,13/70,824/270

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 10/98,13/70,824/270, numerators are 10,13,824

Denominators are 98,70,270

The GCF of 10,13,824 is 1 .

LCM of 98,70,270 is 13230.

The greatest common factor of 10/98,13/70,824/270 = [GCF of 10,13,824]/[LCM of 98,70,270]= 1/13230

Therefore, the GCF of 10/98,13/70,824/270 is 1/13230.

Greatest Common Factor of 10,13,824

To find the highest common factor of 10,13,824, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 13 are 1, 13

The factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824

The HCF of 10,13,824 is 1.

Lets's calculate GCF of 10,13,824

Greatest Common Factor (GCF) of 10,13,824 By Common Division

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

Greatest Common Factor of 10,13,824 By Matching Biggest Common Factor Method

Now, list down the factors of 10

1,2,5,10

Now, list down the factors of 13

1,13

Now, list down the factors of 824

1,2,4,8,103,206,412,824

Greatest Common Factor

We found the factors 10,13,824 . The biggest common factor number is the GCF number.
So the greatest common factor 10,13,824 is 1.

Lets's calculate LCM of 98,70,270

Lowest Common Multiple of 98,70,270 using Common Division

2	98, 70, 270
5	49, 35, 135
7	49, 7, 27
	1, 7, 27

∴ So the LCM of the given numbers is 2 x 5 x 7 x 1 x 7 x 27 = 13230

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13230

Therefore, the GCF of Fractions 10/98,13/70,824/270 is 1/13230

Least Common Multiple of 98,70,270 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 98,70,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(98,70,270) = 2

common factors(in case of two or more numbers have common factors) = 70

GCF(98,70,270) x common factors =2 x 70 = 140

LCM(98,70,270) = ( 98 × 70 × 270 ) / 140

LCM(98,70,270) = 1852200 / 140

LCM(98,70,270) = 13230

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 10/98, 13/70, 824/270

1. What is the HCF of 10,13,824?

The HCF of 10,13,824 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 10/98, 13/70, 824/270?

Answer: GCF of Numerators as per given numbers 10/98, 13/70, 824/270 is

GCF of Numerators i.e. for 10,13,824 is 1

LCM of denominators i.e. for 98,70,270 is 13230.

Thus, GCF of Fractions is 1/13230.Finally, GCF of Fractions for 10/98, 13/70, 824/270 is 1/13230.