How to Find GCF of 730/978, 2117/9182?

GCF of 730/978, 2117/9182

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 730/978, 2117/9182 i.e 73/4489998 easily. The following is the detailed procedure to determine the greatest common factor of fractions 730/978, 2117/9182.

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 730/978,2117/9182?

Given fractions are 730/978,2117/9182

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 730/978,2117/9182, numerators are 730,2117

Denominators are 978,9182

The GCF of 730,2117 is 73 .

LCM of 978,9182 is 4489998.

The greatest common factor of 730/978,2117/9182 = [GCF of 730,2117]/[LCM of 978,9182]= 73/4489998

Therefore, the GCF of 730/978,2117/9182 is 73/4489998.

Greatest Common Factor of 730,2117

To find the highest common factor of 730,2117, we have to find the factors of both numbers and list the highest common factor.

The factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730

The factors of 2117 are 1, 29, 73, 2117

The HCF of 730,2117 is 73.

Lets's calculate GCF of 730,2117

Greatest Common Factor (GCF) of 730,2117 By Common Division

73	730, 2117
	10, 29

∴ So the GCF of the given numbers is 73 = 73

Greatest Common Factor of 730,2117 By Matching Biggest Common Factor Method

Now, list down the factors of 730

1,2,5,10,73,146,365,730

Now, list down the factors of 2117

1,29,73,2117

Greatest Common Factor

We found the factors 730,2117 . The biggest common factor number is the GCF number.
So the greatest common factor 730,2117 is 73.

Lets's calculate LCM of 978,9182

Lowest Common Multiple of 978,9182 using Common Division

2	978, 9182
	489, 4591

∴ So the LCM of the given numbers is 2 x 489 x 4591 = 4489998

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 73/4489998

Therefore, the GCF of Fractions 730/978,2117/9182 is 73/4489998

Least Common Multiple of 978,9182 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 978,9182 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(978,9182) = 2

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

GCF(978,9182) x common factors =2 x 1 = 2

LCM(978,9182) = ( 978 × 9182 ) / 2

LCM(978,9182) = 8979996 / 2

LCM(978,9182) = 4489998

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 730/978, 2117/9182

1. What is the HCF of 730,2117?

The HCF of 730,2117 is 73

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 730/978, 2117/9182?

Answer: GCF of Numerators as per given numbers 730/978, 2117/9182 is

GCF of Numerators i.e. for 730,2117 is 73

LCM of denominators i.e. for 978,9182 is 4489998.

Thus, GCF of Fractions is 73/4489998.Finally, GCF of Fractions for 730/978, 2117/9182 is 73/4489998.