How to Find GCF of 3009/748, 7669/204?

GCF of 3009/748, 7669/204

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 3009/748, 7669/204 i.e 1/2244 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3009/748, 7669/204.

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 3009/748,7669/204?

Given fractions are 3009/748,7669/204

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 3009/748,7669/204, numerators are 3009,7669

Denominators are 748,204

The GCF of 3009,7669 is 1 .

LCM of 748,204 is 2244.

The greatest common factor of 3009/748,7669/204 = [GCF of 3009,7669]/[LCM of 748,204]= 1/2244

Therefore, the GCF of 3009/748,7669/204 is 1/2244.

Greatest Common Factor of 3009,7669

To find the highest common factor of 3009,7669, we have to find the factors of both numbers and list the highest common factor.

The factors of 3009 are 1, 3, 17, 51, 59, 177, 1003, 3009

The factors of 7669 are 1, 7669

The HCF of 3009,7669 is 1.

Lets's calculate GCF of 3009,7669

Greatest Common Factor (GCF) of 3009,7669 By Common Division

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

Greatest Common Factor of 3009,7669 By Matching Biggest Common Factor Method

Now, list down the factors of 3009

1,3,17,51,59,177,1003,3009

Now, list down the factors of 7669

1,7669

Greatest Common Factor

We found the factors 3009,7669 . The biggest common factor number is the GCF number.
So the greatest common factor 3009,7669 is 1.

Lets's calculate LCM of 748,204

Lowest Common Multiple of 748,204 using Common Division

2	748, 204
2	374, 102
17	187, 51
	11, 3

∴ So the LCM of the given numbers is 2 x 2 x 17 x 11 x 3 = 2244

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2244

Therefore, the GCF of Fractions 3009/748,7669/204 is 1/2244

Least Common Multiple of 748,204 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 748,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(748,204) = 68

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

GCF(748,204) x common factors =68 x 1 = 68

LCM(748,204) = ( 748 × 204 ) / 68

LCM(748,204) = 152592 / 68

LCM(748,204) = 2244

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FAQs on GCF of Fractions of 3009/748, 7669/204

1. What is the HCF of 3009,7669?

The HCF of 3009,7669 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 3009/748, 7669/204?

Answer: GCF of Numerators as per given numbers 3009/748, 7669/204 is

GCF of Numerators i.e. for 3009,7669 is 1

LCM of denominators i.e. for 748,204 is 2244.

Thus, GCF of Fractions is 1/2244.Finally, GCF of Fractions for 3009/748, 7669/204 is 1/2244.