How to Find GCF of 18/31, 60/26, 107/470?

GCF of 18/31, 60/26, 107/470

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 18/31, 60/26, 107/470 i.e 1/189410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 18/31, 60/26, 107/470.

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 18/31,60/26,107/470?

Given fractions are 18/31,60/26,107/470

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 18/31,60/26,107/470, numerators are 18,60,107

Denominators are 31,26,470

The GCF of 18,60,107 is 1 .

LCM of 31,26,470 is 189410.

The greatest common factor of 18/31,60/26,107/470 = [GCF of 18,60,107]/[LCM of 31,26,470]= 1/189410

Therefore, the GCF of 18/31,60/26,107/470 is 1/189410.

Greatest Common Factor of 18,60,107

To find the highest common factor of 18,60,107, we have to find the factors of both numbers and list the highest common factor.

The factors of 18 are 1, 2, 3, 6, 9, 18

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 107 are 1, 107

The HCF of 18,60,107 is 1.

Lets's calculate GCF of 18,60,107

Greatest Common Factor (GCF) of 18,60,107 By Common Division

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

Greatest Common Factor of 18,60,107 By Matching Biggest Common Factor Method

Now, list down the factors of 18

1,2,3,6,9,18

Now, list down the factors of 60

1,2,3,4,5,6,10,12,15,20,30,60

Now, list down the factors of 107

1,107

Greatest Common Factor

We found the factors 18,60,107 . The biggest common factor number is the GCF number.
So the greatest common factor 18,60,107 is 1.

Lets's calculate LCM of 31,26,470

Lowest Common Multiple of 31,26,470 using Common Division

2	31, 26, 470
	31, 13, 235

∴ So the LCM of the given numbers is 2 x 31 x 13 x 235 = 189410

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/189410

Therefore, the GCF of Fractions 18/31,60/26,107/470 is 1/189410

Least Common Multiple of 31,26,470 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 31,26,470 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,26,470) = 1

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

GCF(31,26,470) x common factors =1 x 2 = 2

LCM(31,26,470) = ( 31 × 26 × 470 ) / 2

LCM(31,26,470) = 378820 / 2

LCM(31,26,470) = 189410

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 18/31, 60/26, 107/470

1. What is the HCF of 18,60,107?

The HCF of 18,60,107 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 18/31, 60/26, 107/470?

Answer: GCF of Numerators as per given numbers 18/31, 60/26, 107/470 is

GCF of Numerators i.e. for 18,60,107 is 1

LCM of denominators i.e. for 31,26,470 is 189410.

Thus, GCF of Fractions is 1/189410.Finally, GCF of Fractions for 18/31, 60/26, 107/470 is 1/189410.