How to Find GCF of 1730/428, 8300/903?

GCF of 1730/428, 8300/903

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 1730/428, 8300/903 i.e 10/386484 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1730/428, 8300/903.

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 1730/428,8300/903?

Given fractions are 1730/428,8300/903

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 1730/428,8300/903, numerators are 1730,8300

Denominators are 428,903

The GCF of 1730,8300 is 10 .

LCM of 428,903 is 386484.

The greatest common factor of 1730/428,8300/903 = [GCF of 1730,8300]/[LCM of 428,903]= 10/386484

Therefore, the GCF of 1730/428,8300/903 is 10/386484.

Greatest Common Factor of 1730,8300

To find the highest common factor of 1730,8300, we have to find the factors of both numbers and list the highest common factor.

The factors of 1730 are 1, 2, 5, 10, 173, 346, 865, 1730

The factors of 8300 are 1, 2, 4, 5, 10, 20, 25, 50, 83, 100, 166, 332, 415, 830, 1660, 2075, 4150, 8300

The HCF of 1730,8300 is 10.

Lets's calculate GCF of 1730,8300

Greatest Common Factor (GCF) of 1730,8300 By Common Division

2	1730, 8300
5	865, 4150
	173, 830

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 1730,8300 By Matching Biggest Common Factor Method

Now, list down the factors of 1730

1,2,5,10,173,346,865,1730

Now, list down the factors of 8300

1,2,4,5,10,20,25,50,83,100,166,332,415,830,1660,2075,4150,8300

Greatest Common Factor

We found the factors 1730,8300 . The biggest common factor number is the GCF number.
So the greatest common factor 1730,8300 is 10.

Lets's calculate LCM of 428,903

Lowest Common Multiple of 428,903 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 386484

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/386484

Therefore, the GCF of Fractions 1730/428,8300/903 is 10/386484

Least Common Multiple of 428,903 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 428,903 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(428,903) = 1

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

GCF(428,903) x common factors =1 x 1 = 1

LCM(428,903) = ( 428 × 903 ) / 1

LCM(428,903) = 386484 / 1

LCM(428,903) = 386484

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FAQs on GCF of Fractions of 1730/428, 8300/903

1. What is the HCF of 1730,8300?

The HCF of 1730,8300 is 10

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 1730/428, 8300/903?

Answer: GCF of Numerators as per given numbers 1730/428, 8300/903 is

GCF of Numerators i.e. for 1730,8300 is 10

LCM of denominators i.e. for 428,903 is 386484.

Thus, GCF of Fractions is 10/386484.Finally, GCF of Fractions for 1730/428, 8300/903 is 10/386484.