How to Find GCF of 3677/470, 3470/2890?

GCF of 3677/470, 3470/2890

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 3677/470, 3470/2890 i.e 1/135830 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3677/470, 3470/2890.

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 3677/470,3470/2890?

Given fractions are 3677/470,3470/2890

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 3677/470,3470/2890, numerators are 3677,3470

Denominators are 470,2890

The GCF of 3677,3470 is 1 .

LCM of 470,2890 is 135830.

The greatest common factor of 3677/470,3470/2890 = [GCF of 3677,3470]/[LCM of 470,2890]= 1/135830

Therefore, the GCF of 3677/470,3470/2890 is 1/135830.

Greatest Common Factor of 3677,3470

To find the highest common factor of 3677,3470, we have to find the factors of both numbers and list the highest common factor.

The factors of 3677 are 1, 3677

The factors of 3470 are 1, 2, 5, 10, 347, 694, 1735, 3470

The HCF of 3677,3470 is 1.

Lets's calculate GCF of 3677,3470

Greatest Common Factor (GCF) of 3677,3470 By Common Division

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

Greatest Common Factor of 3677,3470 By Matching Biggest Common Factor Method

Now, list down the factors of 3677

1,3677

Now, list down the factors of 3470

1,2,5,10,347,694,1735,3470

Greatest Common Factor

We found the factors 3677,3470 . The biggest common factor number is the GCF number.
So the greatest common factor 3677,3470 is 1.

Lets's calculate LCM of 470,2890

Lowest Common Multiple of 470,2890 using Common Division

2	470, 2890
5	235, 1445
	47, 289

∴ So the LCM of the given numbers is 2 x 5 x 47 x 289 = 135830

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/135830

Therefore, the GCF of Fractions 3677/470,3470/2890 is 1/135830

Least Common Multiple of 470,2890 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 470,2890 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(470,2890) = 10

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

GCF(470,2890) x common factors =10 x 1 = 10

LCM(470,2890) = ( 470 × 2890 ) / 10

LCM(470,2890) = 1358300 / 10

LCM(470,2890) = 135830

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FAQs on GCF of Fractions of 3677/470, 3470/2890

1. What is the HCF of 3677,3470?

The HCF of 3677,3470 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 3677/470, 3470/2890?

Answer: GCF of Numerators as per given numbers 3677/470, 3470/2890 is

GCF of Numerators i.e. for 3677,3470 is 1

LCM of denominators i.e. for 470,2890 is 135830.

Thus, GCF of Fractions is 1/135830.Finally, GCF of Fractions for 3677/470, 3470/2890 is 1/135830.