How to Find GCF of 390/465, 830/619?

GCF of 390/465, 830/619

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 390/465, 830/619 i.e 10/287835 easily. The following is the detailed procedure to determine the greatest common factor of fractions 390/465, 830/619.

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 390/465,830/619?

Given fractions are 390/465,830/619

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 390/465,830/619, numerators are 390,830

Denominators are 465,619

The GCF of 390,830 is 10 .

LCM of 465,619 is 287835.

The greatest common factor of 390/465,830/619 = [GCF of 390,830]/[LCM of 465,619]= 10/287835

Therefore, the GCF of 390/465,830/619 is 10/287835.

Greatest Common Factor of 390,830

To find the highest common factor of 390,830, we have to find the factors of both numbers and list the highest common factor.

The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390

The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830

The HCF of 390,830 is 10.

Lets's calculate GCF of 390,830

Greatest Common Factor (GCF) of 390,830 By Common Division

2	390, 830
5	195, 415
	39, 83

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 390,830 By Matching Biggest Common Factor Method

Now, list down the factors of 390

1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390

Now, list down the factors of 830

1,2,5,10,83,166,415,830

Greatest Common Factor

We found the factors 390,830 . The biggest common factor number is the GCF number.
So the greatest common factor 390,830 is 10.

Lets's calculate LCM of 465,619

Lowest Common Multiple of 465,619 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 287835

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/287835

Therefore, the GCF of Fractions 390/465,830/619 is 10/287835

Least Common Multiple of 465,619 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 465,619 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(465,619) = 1

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

GCF(465,619) x common factors =1 x 1 = 1

LCM(465,619) = ( 465 × 619 ) / 1

LCM(465,619) = 287835 / 1

LCM(465,619) = 287835

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FAQs on GCF of Fractions of 390/465, 830/619

1. What is the HCF of 390,830?

The HCF of 390,830 is 10

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 390/465, 830/619?

Answer: GCF of Numerators as per given numbers 390/465, 830/619 is

GCF of Numerators i.e. for 390,830 is 10

LCM of denominators i.e. for 465,619 is 287835.

Thus, GCF of Fractions is 10/287835.Finally, GCF of Fractions for 390/465, 830/619 is 10/287835.