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GCF of 184/40, 821/342

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 184/40, 821/342 i.e 1/6840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 184/40, 821/342.

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 184/40,821/342?

Given fractions are 184/40,821/342

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 184/40,821/342, numerators are 184,821

Denominators are 40,342

The GCF of 184,821 is 1 .

LCM of 40,342 is 6840.

The greatest common factor of 184/40,821/342 = [GCF of 184,821]/[LCM of 40,342]= 1/6840

Therefore, the GCF of 184/40,821/342 is 1/6840.

Greatest Common Factor of 184,821

To find the highest common factor of 184,821, we have to find the factors of both numbers and list the highest common factor.

The factors of 184 are 1, 2, 4, 8, 23, 46, 92, 184

The factors of 821 are 1, 821

The HCF of 184,821 is 1.

Lets's calculate GCF of 184,821

Greatest Common Factor (GCF) of 184,821 By Common Division

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

Greatest Common Factor of 184,821 By Matching Biggest Common Factor Method

Greatest Common Factor of 184,821 By Matching Biggest Common Factor Method

Now, list down the factors of 184

:

1,2,4,8,23,46,92,184

Now, list down the factors of 821

:

1,821

Greatest Common Factor

We found the factors 184,821 . The biggest common factor number is the GCF number.
So the greatest common factor 184,821 is 1.

Lets's calculate LCM of 40,342

Lowest Common Multiple of 40,342 using Common Division

2 40, 342
20, 171

∴ So the LCM of the given numbers is 2 x 20 x 171 = 6840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6840

Therefore, the GCF of Fractions 184/40,821/342 is 1/6840

Least Common Multiple of 40,342 with GCF Formula

Least Common Multiple of 40,342 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 40,342 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,342) = 2

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

GCF(40,342) x common factors =2 x 1 = 2

LCM(40,342) = ( 40 × 342 ) / 2

LCM(40,342) = 13680 / 2

LCM(40,342) = 6840


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FAQs on GCF of Fractions of 184/40, 821/342

1. What is the HCF of 184,821?

The HCF of 184,821 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 184/40, 821/342?

Answer: GCF of Numerators as per given numbers 184/40, 821/342 is

GCF of Numerators i.e. for 184,821 is 1

LCM of denominators i.e. for 40,342 is 6840.

Thus, GCF of Fractions is 1/6840.Finally, GCF of Fractions for 184/40, 821/342 is 1/6840.