How to Find GCF of 3657/284, 4313/2084?

GCF of 3657/284, 4313/2084

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 3657/284, 4313/2084 i.e 1/147964 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3657/284, 4313/2084.

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 3657/284,4313/2084?

Given fractions are 3657/284,4313/2084

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 3657/284,4313/2084, numerators are 3657,4313

Denominators are 284,2084

The GCF of 3657,4313 is 1 .

LCM of 284,2084 is 147964.

The greatest common factor of 3657/284,4313/2084 = [GCF of 3657,4313]/[LCM of 284,2084]= 1/147964

Therefore, the GCF of 3657/284,4313/2084 is 1/147964.

Greatest Common Factor of 3657,4313

To find the highest common factor of 3657,4313, we have to find the factors of both numbers and list the highest common factor.

The factors of 3657 are 1, 3, 23, 53, 69, 159, 1219, 3657

The factors of 4313 are 1, 19, 227, 4313

The HCF of 3657,4313 is 1.

Lets's calculate GCF of 3657,4313

Greatest Common Factor (GCF) of 3657,4313 By Common Division

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

Greatest Common Factor of 3657,4313 By Matching Biggest Common Factor Method

Now, list down the factors of 3657

1,3,23,53,69,159,1219,3657

Now, list down the factors of 4313

1,19,227,4313

Greatest Common Factor

We found the factors 3657,4313 . The biggest common factor number is the GCF number.
So the greatest common factor 3657,4313 is 1.

Lets's calculate LCM of 284,2084

Lowest Common Multiple of 284,2084 using Common Division

2	284, 2084
2	142, 1042
	71, 521

∴ So the LCM of the given numbers is 2 x 2 x 71 x 521 = 147964

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/147964

Therefore, the GCF of Fractions 3657/284,4313/2084 is 1/147964

Least Common Multiple of 284,2084 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 284,2084 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(284,2084) = 4

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

GCF(284,2084) x common factors =4 x 1 = 4

LCM(284,2084) = ( 284 × 2084 ) / 4

LCM(284,2084) = 591856 / 4

LCM(284,2084) = 147964

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FAQs on GCF of Fractions of 3657/284, 4313/2084

1. What is the HCF of 3657,4313?

The HCF of 3657,4313 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 3657/284, 4313/2084?

Answer: GCF of Numerators as per given numbers 3657/284, 4313/2084 is

GCF of Numerators i.e. for 3657,4313 is 1

LCM of denominators i.e. for 284,2084 is 147964.

Thus, GCF of Fractions is 1/147964.Finally, GCF of Fractions for 3657/284, 4313/2084 is 1/147964.