How to Find GCF of 9739/132, 7470/8204?

GCF of 9739/132, 7470/8204

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 9739/132, 7470/8204 i.e 1/270732 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9739/132, 7470/8204.

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 9739/132,7470/8204?

Given fractions are 9739/132,7470/8204

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 9739/132,7470/8204, numerators are 9739,7470

Denominators are 132,8204

The GCF of 9739,7470 is 1 .

LCM of 132,8204 is 270732.

The greatest common factor of 9739/132,7470/8204 = [GCF of 9739,7470]/[LCM of 132,8204]= 1/270732

Therefore, the GCF of 9739/132,7470/8204 is 1/270732.

Greatest Common Factor of 9739,7470

To find the highest common factor of 9739,7470, we have to find the factors of both numbers and list the highest common factor.

The factors of 9739 are 1, 9739

The factors of 7470 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 83, 90, 166, 249, 415, 498, 747, 830, 1245, 1494, 2490, 3735, 7470

The HCF of 9739,7470 is 1.

Lets's calculate GCF of 9739,7470

Greatest Common Factor (GCF) of 9739,7470 By Common Division

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

Greatest Common Factor of 9739,7470 By Matching Biggest Common Factor Method

Now, list down the factors of 9739

1,9739

Now, list down the factors of 7470

1,2,3,5,6,9,10,15,18,30,45,83,90,166,249,415,498,747,830,1245,1494,2490,3735,7470

Greatest Common Factor

We found the factors 9739,7470 . The biggest common factor number is the GCF number.
So the greatest common factor 9739,7470 is 1.

Lets's calculate LCM of 132,8204

Lowest Common Multiple of 132,8204 using Common Division

2	132, 8204
2	66, 4102
	33, 2051

∴ So the LCM of the given numbers is 2 x 2 x 33 x 2051 = 270732

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/270732

Therefore, the GCF of Fractions 9739/132,7470/8204 is 1/270732

Least Common Multiple of 132,8204 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 132,8204 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(132,8204) = 4

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

GCF(132,8204) x common factors =4 x 1 = 4

LCM(132,8204) = ( 132 × 8204 ) / 4

LCM(132,8204) = 1082928 / 4

LCM(132,8204) = 270732

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 9739/132, 7470/8204

1. What is the HCF of 9739,7470?

The HCF of 9739,7470 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 9739/132, 7470/8204?

Answer: GCF of Numerators as per given numbers 9739/132, 7470/8204 is

GCF of Numerators i.e. for 9739,7470 is 1

LCM of denominators i.e. for 132,8204 is 270732.

Thus, GCF of Fractions is 1/270732.Finally, GCF of Fractions for 9739/132, 7470/8204 is 1/270732.