How to Find GCF of 190/649, 519/661?

GCF of 190/649, 519/661

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 190/649, 519/661 i.e 1/428989 easily. The following is the detailed procedure to determine the greatest common factor of fractions 190/649, 519/661.

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 190/649,519/661?

Given fractions are 190/649,519/661

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 190/649,519/661, numerators are 190,519

Denominators are 649,661

The GCF of 190,519 is 1 .

LCM of 649,661 is 428989.

The greatest common factor of 190/649,519/661 = [GCF of 190,519]/[LCM of 649,661]= 1/428989

Therefore, the GCF of 190/649,519/661 is 1/428989.

Greatest Common Factor of 190,519

To find the highest common factor of 190,519, we have to find the factors of both numbers and list the highest common factor.

The factors of 190 are 1, 2, 5, 10, 19, 38, 95, 190

The factors of 519 are 1, 3, 173, 519

The HCF of 190,519 is 1.

Lets's calculate GCF of 190,519

Greatest Common Factor (GCF) of 190,519 By Common Division

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

Greatest Common Factor of 190,519 By Matching Biggest Common Factor Method

Now, list down the factors of 190

1,2,5,10,19,38,95,190

Now, list down the factors of 519

1,3,173,519

Greatest Common Factor

We found the factors 190,519 . The biggest common factor number is the GCF number.
So the greatest common factor 190,519 is 1.

Lets's calculate LCM of 649,661

Lowest Common Multiple of 649,661 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 428989

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/428989

Therefore, the GCF of Fractions 190/649,519/661 is 1/428989

Least Common Multiple of 649,661 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 649,661 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(649,661) = 1

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

GCF(649,661) x common factors =1 x 1 = 1

LCM(649,661) = ( 649 × 661 ) / 1

LCM(649,661) = 428989 / 1

LCM(649,661) = 428989

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FAQs on GCF of Fractions of 190/649, 519/661

1. What is the HCF of 190,519?

The HCF of 190,519 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 190/649, 519/661?

Answer: GCF of Numerators as per given numbers 190/649, 519/661 is

GCF of Numerators i.e. for 190,519 is 1

LCM of denominators i.e. for 649,661 is 428989.

Thus, GCF of Fractions is 1/428989.Finally, GCF of Fractions for 190/649, 519/661 is 1/428989.