How to Find GCF of 1749/470, 8870/9742?

GCF of 1749/470, 8870/9742

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 1749/470, 8870/9742 i.e 1/2289370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1749/470, 8870/9742.

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 1749/470,8870/9742?

Given fractions are 1749/470,8870/9742

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 1749/470,8870/9742, numerators are 1749,8870

Denominators are 470,9742

The GCF of 1749,8870 is 1 .

LCM of 470,9742 is 2289370.

The greatest common factor of 1749/470,8870/9742 = [GCF of 1749,8870]/[LCM of 470,9742]= 1/2289370

Therefore, the GCF of 1749/470,8870/9742 is 1/2289370.

Greatest Common Factor of 1749,8870

To find the highest common factor of 1749,8870, we have to find the factors of both numbers and list the highest common factor.

The factors of 1749 are 1, 3, 11, 33, 53, 159, 583, 1749

The factors of 8870 are 1, 2, 5, 10, 887, 1774, 4435, 8870

The HCF of 1749,8870 is 1.

Lets's calculate GCF of 1749,8870

Greatest Common Factor (GCF) of 1749,8870 By Common Division

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

Greatest Common Factor of 1749,8870 By Matching Biggest Common Factor Method

Now, list down the factors of 1749

1,3,11,33,53,159,583,1749

Now, list down the factors of 8870

1,2,5,10,887,1774,4435,8870

Greatest Common Factor

We found the factors 1749,8870 . The biggest common factor number is the GCF number.
So the greatest common factor 1749,8870 is 1.

Lets's calculate LCM of 470,9742

Lowest Common Multiple of 470,9742 using Common Division

2	470, 9742
	235, 4871

∴ So the LCM of the given numbers is 2 x 235 x 4871 = 2289370

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2289370

Therefore, the GCF of Fractions 1749/470,8870/9742 is 1/2289370

Least Common Multiple of 470,9742 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 470,9742 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(470,9742) = 2

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

GCF(470,9742) x common factors =2 x 1 = 2

LCM(470,9742) = ( 470 × 9742 ) / 2

LCM(470,9742) = 4578740 / 2

LCM(470,9742) = 2289370

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 1749/470, 8870/9742

1. What is the HCF of 1749,8870?

The HCF of 1749,8870 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 1749/470, 8870/9742?

Answer: GCF of Numerators as per given numbers 1749/470, 8870/9742 is

GCF of Numerators i.e. for 1749,8870 is 1

LCM of denominators i.e. for 470,9742 is 2289370.

Thus, GCF of Fractions is 1/2289370.Finally, GCF of Fractions for 1749/470, 8870/9742 is 1/2289370.