How to Find GCF of 98/26, 172/43, 380/218?

GCF of 98/26, 172/43, 380/218

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 98/26, 172/43, 380/218 i.e 2/121862 easily. The following is the detailed procedure to determine the greatest common factor of fractions 98/26, 172/43, 380/218.

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 98/26,172/43,380/218?

Given fractions are 98/26,172/43,380/218

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 98/26,172/43,380/218, numerators are 98,172,380

Denominators are 26,43,218

The GCF of 98,172,380 is 2 .

LCM of 26,43,218 is 121862.

The greatest common factor of 98/26,172/43,380/218 = [GCF of 98,172,380]/[LCM of 26,43,218]= 2/121862

Therefore, the GCF of 98/26,172/43,380/218 is 2/121862.

Greatest Common Factor of 98,172,380

To find the highest common factor of 98,172,380, we have to find the factors of both numbers and list the highest common factor.

The factors of 98 are 1, 2, 7, 14, 49, 98

The factors of 172 are 1, 2, 4, 43, 86, 172

The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380

The HCF of 98,172,380 is 2.

Lets's calculate GCF of 98,172,380

Greatest Common Factor (GCF) of 98,172,380 By Common Division

2	98, 172, 380
	49, 86, 190

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

Greatest Common Factor of 98,172,380 By Matching Biggest Common Factor Method

Now, list down the factors of 98

1,2,7,14,49,98

Now, list down the factors of 172

1,2,4,43,86,172

Now, list down the factors of 380

1,2,4,5,10,19,20,38,76,95,190,380

Greatest Common Factor

We found the factors 98,172,380 . The biggest common factor number is the GCF number.
So the greatest common factor 98,172,380 is 2.

Lets's calculate LCM of 26,43,218

Lowest Common Multiple of 26,43,218 using Common Division

2	26, 43, 218
	13, 43, 109

∴ So the LCM of the given numbers is 2 x 13 x 43 x 109 = 121862

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/121862

Therefore, the GCF of Fractions 98/26,172/43,380/218 is 2/121862

Least Common Multiple of 26,43,218 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 26,43,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(26,43,218) = 1

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

GCF(26,43,218) x common factors =1 x 2 = 2

LCM(26,43,218) = ( 26 × 43 × 218 ) / 2

LCM(26,43,218) = 243724 / 2

LCM(26,43,218) = 121862

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 98/26, 172/43, 380/218

1. What is the HCF of 98,172,380?

The HCF of 98,172,380 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 98/26, 172/43, 380/218?

Answer: GCF of Numerators as per given numbers 98/26, 172/43, 380/218 is

GCF of Numerators i.e. for 98,172,380 is 2

LCM of denominators i.e. for 26,43,218 is 121862.

Thus, GCF of Fractions is 2/121862.Finally, GCF of Fractions for 98/26, 172/43, 380/218 is 2/121862.