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GCF of 190/172, 790/289

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 190/172, 790/289 i.e 10/49708 easily. The following is the detailed procedure to determine the greatest common factor of fractions 190/172, 790/289.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 190/172,790/289?

Given fractions are 190/172,790/289

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 190/172,790/289, numerators are 190,790

Denominators are 172,289

The GCF of 190,790 is 10 .

LCM of 172,289 is 49708.

The greatest common factor of 190/172,790/289 = [GCF of 190,790]/[LCM of 172,289]= 10/49708

Therefore, the GCF of 190/172,790/289 is 10/49708.

Greatest Common Factor of 190,790

To find the highest common factor of 190,790, 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 790 are 1, 2, 5, 10, 79, 158, 395, 790

The HCF of 190,790 is 10.

Lets's calculate GCF of 190,790

Greatest Common Factor (GCF) of 190,790 By Common Division

2 190, 790
5 95, 395
19, 79

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

Greatest Common Factor of 190,790 By Matching Biggest Common Factor Method

Greatest Common Factor of 190,790 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 790

:

1,2,5,10,79,158,395,790

Greatest Common Factor

We found the factors 190,790 . The biggest common factor number is the GCF number.
So the greatest common factor 190,790 is 10.

Lets's calculate LCM of 172,289

Lowest Common Multiple of 172,289 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 49708

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/49708

Therefore, the GCF of Fractions 190/172,790/289 is 10/49708

Least Common Multiple of 172,289 with GCF Formula

Least Common Multiple of 172,289 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 172,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(172,289) = 1

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

GCF(172,289) x common factors =1 x 1 = 1

LCM(172,289) = ( 172 × 289 ) / 1

LCM(172,289) = 49708 / 1

LCM(172,289) = 49708


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FAQs on GCF of Fractions of 190/172, 790/289

1. What is the HCF of 190,790?

The HCF of 190,790 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 190/172, 790/289?

Answer: GCF of Numerators as per given numbers 190/172, 790/289 is

GCF of Numerators i.e. for 190,790 is 10

LCM of denominators i.e. for 172,289 is 49708.

Thus, GCF of Fractions is 10/49708.Finally, GCF of Fractions for 190/172, 790/289 is 10/49708.