How to Find GCF of 8227/300, 1125/1244?

GCF of 8227/300, 1125/1244

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 8227/300, 1125/1244 i.e 1/93300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8227/300, 1125/1244.

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 8227/300,1125/1244?

Given fractions are 8227/300,1125/1244

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 8227/300,1125/1244, numerators are 8227,1125

Denominators are 300,1244

The GCF of 8227,1125 is 1 .

LCM of 300,1244 is 93300.

The greatest common factor of 8227/300,1125/1244 = [GCF of 8227,1125]/[LCM of 300,1244]= 1/93300

Therefore, the GCF of 8227/300,1125/1244 is 1/93300.

Greatest Common Factor of 8227,1125

To find the highest common factor of 8227,1125, we have to find the factors of both numbers and list the highest common factor.

The factors of 8227 are 1, 19, 433, 8227

The factors of 1125 are 1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 1125

The HCF of 8227,1125 is 1.

Lets's calculate GCF of 8227,1125

Greatest Common Factor (GCF) of 8227,1125 By Common Division

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

Greatest Common Factor of 8227,1125 By Matching Biggest Common Factor Method

Now, list down the factors of 8227

1,19,433,8227

Now, list down the factors of 1125

1,3,5,9,15,25,45,75,125,225,375,1125

Greatest Common Factor

We found the factors 8227,1125 . The biggest common factor number is the GCF number.
So the greatest common factor 8227,1125 is 1.

Lets's calculate LCM of 300,1244

Lowest Common Multiple of 300,1244 using Common Division

2	300, 1244
2	150, 622
	75, 311

∴ So the LCM of the given numbers is 2 x 2 x 75 x 311 = 93300

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/93300

Therefore, the GCF of Fractions 8227/300,1125/1244 is 1/93300

Least Common Multiple of 300,1244 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 300,1244 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(300,1244) = 4

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

GCF(300,1244) x common factors =4 x 1 = 4

LCM(300,1244) = ( 300 × 1244 ) / 4

LCM(300,1244) = 373200 / 4

LCM(300,1244) = 93300

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FAQs on GCF of Fractions of 8227/300, 1125/1244

1. What is the HCF of 8227,1125?

The HCF of 8227,1125 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 8227/300, 1125/1244?

Answer: GCF of Numerators as per given numbers 8227/300, 1125/1244 is

GCF of Numerators i.e. for 8227,1125 is 1

LCM of denominators i.e. for 300,1244 is 93300.

Thus, GCF of Fractions is 1/93300.Finally, GCF of Fractions for 8227/300, 1125/1244 is 1/93300.