How to Find GCF of 720/465, 656/287?

GCF of 720/465, 656/287

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 720/465, 656/287 i.e 16/133455 easily. The following is the detailed procedure to determine the greatest common factor of fractions 720/465, 656/287.

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 720/465,656/287?

Given fractions are 720/465,656/287

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 720/465,656/287, numerators are 720,656

Denominators are 465,287

The GCF of 720,656 is 16 .

LCM of 465,287 is 133455.

The greatest common factor of 720/465,656/287 = [GCF of 720,656]/[LCM of 465,287]= 16/133455

Therefore, the GCF of 720/465,656/287 is 16/133455.

Greatest Common Factor of 720,656

To find the highest common factor of 720,656, we have to find the factors of both numbers and list the highest common factor.

The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720

The factors of 656 are 1, 2, 4, 8, 16, 41, 82, 164, 328, 656

The HCF of 720,656 is 16.

Lets's calculate GCF of 720,656

Greatest Common Factor (GCF) of 720,656 By Common Division

2	720, 656
2	360, 328
2	180, 164
2	90, 82
	45, 41

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16

Greatest Common Factor of 720,656 By Matching Biggest Common Factor Method

Now, list down the factors of 720

1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720

Now, list down the factors of 656

1,2,4,8,16,41,82,164,328,656

Greatest Common Factor

We found the factors 720,656 . The biggest common factor number is the GCF number.
So the greatest common factor 720,656 is 16.

Lets's calculate LCM of 465,287

Lowest Common Multiple of 465,287 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 133455

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/133455

Therefore, the GCF of Fractions 720/465,656/287 is 16/133455

Least Common Multiple of 465,287 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 465,287 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(465,287) = 1

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

GCF(465,287) x common factors =1 x 1 = 1

LCM(465,287) = ( 465 × 287 ) / 1

LCM(465,287) = 133455 / 1

LCM(465,287) = 133455

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FAQs on GCF of Fractions of 720/465, 656/287

1. What is the HCF of 720,656?

The HCF of 720,656 is 16

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 720/465, 656/287?

Answer: GCF of Numerators as per given numbers 720/465, 656/287 is

GCF of Numerators i.e. for 720,656 is 16

LCM of denominators i.e. for 465,287 is 133455.

Thus, GCF of Fractions is 16/133455.Finally, GCF of Fractions for 720/465, 656/287 is 16/133455.