How to Find GCF of 4209/725, 9223/6719?

GCF of 4209/725, 9223/6719

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 4209/725, 9223/6719 i.e 23/4871275 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4209/725, 9223/6719.

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 4209/725,9223/6719?

Given fractions are 4209/725,9223/6719

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 4209/725,9223/6719, numerators are 4209,9223

Denominators are 725,6719

The GCF of 4209,9223 is 23 .

LCM of 725,6719 is 4871275.

The greatest common factor of 4209/725,9223/6719 = [GCF of 4209,9223]/[LCM of 725,6719]= 23/4871275

Therefore, the GCF of 4209/725,9223/6719 is 23/4871275.

Greatest Common Factor of 4209,9223

To find the highest common factor of 4209,9223, we have to find the factors of both numbers and list the highest common factor.

The factors of 4209 are 1, 3, 23, 61, 69, 183, 1403, 4209

The factors of 9223 are 1, 23, 401, 9223

The HCF of 4209,9223 is 23.

Lets's calculate GCF of 4209,9223

Greatest Common Factor (GCF) of 4209,9223 By Common Division

23	4209, 9223
	183, 401

∴ So the GCF of the given numbers is 23 = 23

Greatest Common Factor of 4209,9223 By Matching Biggest Common Factor Method

Now, list down the factors of 4209

1,3,23,61,69,183,1403,4209

Now, list down the factors of 9223

1,23,401,9223

Greatest Common Factor

We found the factors 4209,9223 . The biggest common factor number is the GCF number.
So the greatest common factor 4209,9223 is 23.

Lets's calculate LCM of 725,6719

Lowest Common Multiple of 725,6719 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 4871275

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/4871275

Therefore, the GCF of Fractions 4209/725,9223/6719 is 23/4871275

Least Common Multiple of 725,6719 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 725,6719 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(725,6719) = 1

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

GCF(725,6719) x common factors =1 x 1 = 1

LCM(725,6719) = ( 725 × 6719 ) / 1

LCM(725,6719) = 4871275 / 1

LCM(725,6719) = 4871275

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FAQs on GCF of Fractions of 4209/725, 9223/6719

1. What is the HCF of 4209,9223?

The HCF of 4209,9223 is 23

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 4209/725, 9223/6719?

Answer: GCF of Numerators as per given numbers 4209/725, 9223/6719 is

GCF of Numerators i.e. for 4209,9223 is 23

LCM of denominators i.e. for 725,6719 is 4871275.

Thus, GCF of Fractions is 23/4871275.Finally, GCF of Fractions for 4209/725, 9223/6719 is 23/4871275.