How to Find GCF of 2420/284, 3762/1649?

GCF of 2420/284, 3762/1649

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 2420/284, 3762/1649 i.e 22/468316 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2420/284, 3762/1649.

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 2420/284,3762/1649?

Given fractions are 2420/284,3762/1649

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 2420/284,3762/1649, numerators are 2420,3762

Denominators are 284,1649

The GCF of 2420,3762 is 22 .

LCM of 284,1649 is 468316.

The greatest common factor of 2420/284,3762/1649 = [GCF of 2420,3762]/[LCM of 284,1649]= 22/468316

Therefore, the GCF of 2420/284,3762/1649 is 22/468316.

Greatest Common Factor of 2420,3762

To find the highest common factor of 2420,3762, we have to find the factors of both numbers and list the highest common factor.

The factors of 2420 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 121, 220, 242, 484, 605, 1210, 2420

The factors of 3762 are 1, 2, 3, 6, 9, 11, 18, 19, 22, 33, 38, 57, 66, 99, 114, 171, 198, 209, 342, 418, 627, 1254, 1881, 3762

The HCF of 2420,3762 is 22.

Lets's calculate GCF of 2420,3762

Greatest Common Factor (GCF) of 2420,3762 By Common Division

2	2420, 3762
11	1210, 1881
	110, 171

∴ So the GCF of the given numbers is 2 x 11 = 22

Greatest Common Factor of 2420,3762 By Matching Biggest Common Factor Method

Now, list down the factors of 2420

1,2,4,5,10,11,20,22,44,55,110,121,220,242,484,605,1210,2420

Now, list down the factors of 3762

1,2,3,6,9,11,18,19,22,33,38,57,66,99,114,171,198,209,342,418,627,1254,1881,3762

Greatest Common Factor

We found the factors 2420,3762 . The biggest common factor number is the GCF number.
So the greatest common factor 2420,3762 is 22.

Lets's calculate LCM of 284,1649

Lowest Common Multiple of 284,1649 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 468316

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/468316

Therefore, the GCF of Fractions 2420/284,3762/1649 is 22/468316

Least Common Multiple of 284,1649 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 284,1649 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(284,1649) = 1

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

GCF(284,1649) x common factors =1 x 1 = 1

LCM(284,1649) = ( 284 × 1649 ) / 1

LCM(284,1649) = 468316 / 1

LCM(284,1649) = 468316

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FAQs on GCF of Fractions of 2420/284, 3762/1649

1. What is the HCF of 2420,3762?

The HCF of 2420,3762 is 22

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 2420/284, 3762/1649?

Answer: GCF of Numerators as per given numbers 2420/284, 3762/1649 is

GCF of Numerators i.e. for 2420,3762 is 22

LCM of denominators i.e. for 284,1649 is 468316.

Thus, GCF of Fractions is 22/468316.Finally, GCF of Fractions for 2420/284, 3762/1649 is 22/468316.