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GCF of 185/412, 215/722

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 185/412, 215/722 i.e 5/148732 easily. The following is the detailed procedure to determine the greatest common factor of fractions 185/412, 215/722.

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 185/412,215/722?

Given fractions are 185/412,215/722

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 185/412,215/722, numerators are 185,215

Denominators are 412,722

The GCF of 185,215 is 5 .

LCM of 412,722 is 148732.

The greatest common factor of 185/412,215/722 = [GCF of 185,215]/[LCM of 412,722]= 5/148732

Therefore, the GCF of 185/412,215/722 is 5/148732.

Greatest Common Factor of 185,215

To find the highest common factor of 185,215, 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 215 are 1, 5, 43, 215

The HCF of 185,215 is 5.

Lets's calculate GCF of 185,215

Greatest Common Factor (GCF) of 185,215 By Common Division

5 185, 215
37, 43

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

Greatest Common Factor of 185,215 By Matching Biggest Common Factor Method

Greatest Common Factor of 185,215 By Matching Biggest Common Factor Method

Now, list down the factors of 185

:

1,5,37,185

Now, list down the factors of 215

:

1,5,43,215

Greatest Common Factor

We found the factors 185,215 . The biggest common factor number is the GCF number.
So the greatest common factor 185,215 is 5.

Lets's calculate LCM of 412,722

Lowest Common Multiple of 412,722 using Common Division

2 412, 722
206, 361

∴ So the LCM of the given numbers is 2 x 206 x 361 = 148732

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/148732

Therefore, the GCF of Fractions 185/412,215/722 is 5/148732

Least Common Multiple of 412,722 with GCF Formula

Least Common Multiple of 412,722 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 412,722 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(412,722) = 2

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

GCF(412,722) x common factors =2 x 1 = 2

LCM(412,722) = ( 412 × 722 ) / 2

LCM(412,722) = 297464 / 2

LCM(412,722) = 148732


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FAQs on GCF of Fractions of 185/412, 215/722

1. What is the HCF of 185,215?

The HCF of 185,215 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 185/412, 215/722?

Answer: GCF of Numerators as per given numbers 185/412, 215/722 is

GCF of Numerators i.e. for 185,215 is 5

LCM of denominators i.e. for 412,722 is 148732.

Thus, GCF of Fractions is 5/148732.Finally, GCF of Fractions for 185/412, 215/722 is 5/148732.