How to Find GCF of 830/392, 5225/816?

GCF of 830/392, 5225/816

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 830/392, 5225/816 i.e 5/39984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 830/392, 5225/816.

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 830/392,5225/816?

Given fractions are 830/392,5225/816

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 830/392,5225/816, numerators are 830,5225

Denominators are 392,816

The GCF of 830,5225 is 5 .

LCM of 392,816 is 39984.

The greatest common factor of 830/392,5225/816 = [GCF of 830,5225]/[LCM of 392,816]= 5/39984

Therefore, the GCF of 830/392,5225/816 is 5/39984.

Greatest Common Factor of 830,5225

To find the highest common factor of 830,5225, we have to find the factors of both numbers and list the highest common factor.

The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830

The factors of 5225 are 1, 5, 11, 19, 25, 55, 95, 209, 275, 475, 1045, 5225

The HCF of 830,5225 is 5.

Lets's calculate GCF of 830,5225

Greatest Common Factor (GCF) of 830,5225 By Common Division

5	830, 5225
	166, 1045

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 830,5225 By Matching Biggest Common Factor Method

Now, list down the factors of 830

1,2,5,10,83,166,415,830

Now, list down the factors of 5225

1,5,11,19,25,55,95,209,275,475,1045,5225

Greatest Common Factor

We found the factors 830,5225 . The biggest common factor number is the GCF number.
So the greatest common factor 830,5225 is 5.

Lets's calculate LCM of 392,816

Lowest Common Multiple of 392,816 using Common Division

2	392, 816
2	196, 408
2	98, 204
	49, 102

∴ So the LCM of the given numbers is 2 x 2 x 2 x 49 x 102 = 39984

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/39984

Therefore, the GCF of Fractions 830/392,5225/816 is 5/39984

Least Common Multiple of 392,816 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 392,816 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(392,816) = 8

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

GCF(392,816) x common factors =8 x 1 = 8

LCM(392,816) = ( 392 × 816 ) / 8

LCM(392,816) = 319872 / 8

LCM(392,816) = 39984

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FAQs on GCF of Fractions of 830/392, 5225/816

1. What is the HCF of 830,5225?

The HCF of 830,5225 is 5

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 830/392, 5225/816?

Answer: GCF of Numerators as per given numbers 830/392, 5225/816 is

GCF of Numerators i.e. for 830,5225 is 5

LCM of denominators i.e. for 392,816 is 39984.

Thus, GCF of Fractions is 5/39984.Finally, GCF of Fractions for 830/392, 5225/816 is 5/39984.