How to Find GCF of 380/998, 420/627?

GCF of 380/998, 420/627

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 380/998, 420/627 i.e 20/625746 easily. The following is the detailed procedure to determine the greatest common factor of fractions 380/998, 420/627.

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 380/998,420/627?

Given fractions are 380/998,420/627

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 380/998,420/627, numerators are 380,420

Denominators are 998,627

The GCF of 380,420 is 20 .

LCM of 998,627 is 625746.

The greatest common factor of 380/998,420/627 = [GCF of 380,420]/[LCM of 998,627]= 20/625746

Therefore, the GCF of 380/998,420/627 is 20/625746.

Greatest Common Factor of 380,420

To find the highest common factor of 380,420, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

The HCF of 380,420 is 20.

Lets's calculate GCF of 380,420

Greatest Common Factor (GCF) of 380,420 By Common Division

2	380, 420
2	190, 210
5	95, 105
	19, 21

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 380,420 By Matching Biggest Common Factor Method

Now, list down the factors of 380

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

Now, list down the factors of 420

1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420

Greatest Common Factor

We found the factors 380,420 . The biggest common factor number is the GCF number.
So the greatest common factor 380,420 is 20.

Lets's calculate LCM of 998,627

Lowest Common Multiple of 998,627 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 625746

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/625746

Therefore, the GCF of Fractions 380/998,420/627 is 20/625746

Least Common Multiple of 998,627 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 998,627 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(998,627) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(998,627) x common factors =1 x 1 = 1

LCM(998,627) = ( 998 × 627 ) / 1

LCM(998,627) = 625746 / 1

LCM(998,627) = 625746

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 380/998, 420/627

1. What is the HCF of 380,420?

The HCF of 380,420 is 20

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 380/998, 420/627?

Answer: GCF of Numerators as per given numbers 380/998, 420/627 is

GCF of Numerators i.e. for 380,420 is 20

LCM of denominators i.e. for 998,627 is 625746.

Thus, GCF of Fractions is 20/625746.Finally, GCF of Fractions for 380/998, 420/627 is 20/625746.