How to Find GCF of 14/860, 21/470, 414/389?

GCF of 14/860, 21/470, 414/389

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 14/860, 21/470, 414/389 i.e 1/15723380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/860, 21/470, 414/389.

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 14/860,21/470,414/389?

Given fractions are 14/860,21/470,414/389

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 14/860,21/470,414/389, numerators are 14,21,414

Denominators are 860,470,389

The GCF of 14,21,414 is 1 .

LCM of 860,470,389 is 15723380.

The greatest common factor of 14/860,21/470,414/389 = [GCF of 14,21,414]/[LCM of 860,470,389]= 1/15723380

Therefore, the GCF of 14/860,21/470,414/389 is 1/15723380.

Greatest Common Factor of 14,21,414

To find the highest common factor of 14,21,414, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 21 are 1, 3, 7, 21

The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

The HCF of 14,21,414 is 1.

Lets's calculate GCF of 14,21,414

Greatest Common Factor (GCF) of 14,21,414 By Common Division

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

Greatest Common Factor of 14,21,414 By Matching Biggest Common Factor Method

Now, list down the factors of 14

1,2,7,14

Now, list down the factors of 21

1,3,7,21

Now, list down the factors of 414

1,2,3,6,9,18,23,46,69,138,207,414

Greatest Common Factor

We found the factors 14,21,414 . The biggest common factor number is the GCF number.
So the greatest common factor 14,21,414 is 1.

Lets's calculate LCM of 860,470,389

Lowest Common Multiple of 860,470,389 using Common Division

2	860, 470, 389
5	430, 235, 389
	86, 47, 389

∴ So the LCM of the given numbers is 2 x 5 x 86 x 47 x 389 = 15723380

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15723380

Therefore, the GCF of Fractions 14/860,21/470,414/389 is 1/15723380

Least Common Multiple of 860,470,389 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 860,470,389 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(860,470,389) = 1

common factors(in case of two or more numbers have common factors) = 10

GCF(860,470,389) x common factors =1 x 10 = 10

LCM(860,470,389) = ( 860 × 470 × 389 ) / 10

LCM(860,470,389) = 157233800 / 10

LCM(860,470,389) = 15723380

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 14/860, 21/470, 414/389

1. What is the HCF of 14,21,414?

The HCF of 14,21,414 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 14/860, 21/470, 414/389?

Answer: GCF of Numerators as per given numbers 14/860, 21/470, 414/389 is

GCF of Numerators i.e. for 14,21,414 is 1

LCM of denominators i.e. for 860,470,389 is 15723380.

Thus, GCF of Fractions is 1/15723380.Finally, GCF of Fractions for 14/860, 21/470, 414/389 is 1/15723380.