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GCF of 185/257, 310/561

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 185/257, 310/561 i.e 5/144177 easily. The following is the detailed procedure to determine the greatest common factor of fractions 185/257, 310/561.

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 185/257,310/561?

Given fractions are 185/257,310/561

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 185/257,310/561, numerators are 185,310

Denominators are 257,561

The GCF of 185,310 is 5 .

LCM of 257,561 is 144177.

The greatest common factor of 185/257,310/561 = [GCF of 185,310]/[LCM of 257,561]= 5/144177

Therefore, the GCF of 185/257,310/561 is 5/144177.

Greatest Common Factor of 185,310

To find the highest common factor of 185,310, we have to find the factors of both numbers and list the highest common factor.

The factors of 185 are 1, 5, 37, 185

The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310

The HCF of 185,310 is 5.

Lets's calculate GCF of 185,310

Greatest Common Factor (GCF) of 185,310 By Common Division

5 185, 310
37, 62

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 185,310 By Matching Biggest Common Factor Method

Greatest Common Factor of 185,310 By Matching Biggest Common Factor Method

Now, list down the factors of 185

:

1,5,37,185

Now, list down the factors of 310

:

1,2,5,10,31,62,155,310

Greatest Common Factor

We found the factors 185,310 . The biggest common factor number is the GCF number.
So the greatest common factor 185,310 is 5.

Lets's calculate LCM of 257,561

Lowest Common Multiple of 257,561 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 144177

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/144177

Therefore, the GCF of Fractions 185/257,310/561 is 5/144177

Least Common Multiple of 257,561 with GCF Formula

Least Common Multiple of 257,561 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 257,561 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(257,561) = 1

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

GCF(257,561) x common factors =1 x 1 = 1

LCM(257,561) = ( 257 × 561 ) / 1

LCM(257,561) = 144177 / 1

LCM(257,561) = 144177


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FAQs on GCF of Fractions of 185/257, 310/561

1. What is the HCF of 185,310?

The HCF of 185,310 is 5

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 185/257, 310/561?

Answer: GCF of Numerators as per given numbers 185/257, 310/561 is

GCF of Numerators i.e. for 185,310 is 5

LCM of denominators i.e. for 257,561 is 144177.

Thus, GCF of Fractions is 5/144177.Finally, GCF of Fractions for 185/257, 310/561 is 5/144177.