How to Find GCF of 206/726, 300/264?

GCF of 206/726, 300/264

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 206/726, 300/264 i.e 2/2904 easily. The following is the detailed procedure to determine the greatest common factor of fractions 206/726, 300/264.

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 206/726,300/264?

Given fractions are 206/726,300/264

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 206/726,300/264, numerators are 206,300

Denominators are 726,264

The GCF of 206,300 is 2 .

LCM of 726,264 is 2904.

The greatest common factor of 206/726,300/264 = [GCF of 206,300]/[LCM of 726,264]= 2/2904

Therefore, the GCF of 206/726,300/264 is 2/2904.

Greatest Common Factor of 206,300

To find the highest common factor of 206,300, we have to find the factors of both numbers and list the highest common factor.

The factors of 206 are 1, 2, 103, 206

The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

The HCF of 206,300 is 2.

Lets's calculate GCF of 206,300

Greatest Common Factor (GCF) of 206,300 By Common Division

2	206, 300
	103, 150

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 206,300 By Matching Biggest Common Factor Method

Now, list down the factors of 206

1,2,103,206

Now, list down the factors of 300

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Greatest Common Factor

We found the factors 206,300 . The biggest common factor number is the GCF number.
So the greatest common factor 206,300 is 2.

Lets's calculate LCM of 726,264

Lowest Common Multiple of 726,264 using Common Division

2	726, 264
3	363, 132
11	121, 44
	11, 4

∴ So the LCM of the given numbers is 2 x 3 x 11 x 11 x 4 = 2904

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2904

Therefore, the GCF of Fractions 206/726,300/264 is 2/2904

Least Common Multiple of 726,264 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 726,264 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(726,264) = 66

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

GCF(726,264) x common factors =66 x 1 = 66

LCM(726,264) = ( 726 × 264 ) / 66

LCM(726,264) = 191664 / 66

LCM(726,264) = 2904

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FAQs on GCF of Fractions of 206/726, 300/264

1. What is the HCF of 206,300?

The HCF of 206,300 is 2

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 206/726, 300/264?

Answer: GCF of Numerators as per given numbers 206/726, 300/264 is

GCF of Numerators i.e. for 206,300 is 2

LCM of denominators i.e. for 726,264 is 2904.

Thus, GCF of Fractions is 2/2904.Finally, GCF of Fractions for 206/726, 300/264 is 2/2904.