How to Find GCF of 800/277, 224/280?

GCF of 800/277, 224/280

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 800/277, 224/280 i.e 32/77560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 800/277, 224/280.

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 800/277,224/280?

Given fractions are 800/277,224/280

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 800/277,224/280, numerators are 800,224

Denominators are 277,280

The GCF of 800,224 is 32 .

LCM of 277,280 is 77560.

The greatest common factor of 800/277,224/280 = [GCF of 800,224]/[LCM of 277,280]= 32/77560

Therefore, the GCF of 800/277,224/280 is 32/77560.

Greatest Common Factor of 800,224

To find the highest common factor of 800,224, we have to find the factors of both numbers and list the highest common factor.

The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800

The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224

The HCF of 800,224 is 32.

Lets's calculate GCF of 800,224

Greatest Common Factor (GCF) of 800,224 By Common Division

2	800, 224
2	400, 112
2	200, 56
2	100, 28
2	50, 14
	25, 7

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32

Greatest Common Factor of 800,224 By Matching Biggest Common Factor Method

Now, list down the factors of 800

1,2,4,5,8,10,16,20,25,32,40,50,80,100,160,200,400,800

Now, list down the factors of 224

1,2,4,7,8,14,16,28,32,56,112,224

Greatest Common Factor

We found the factors 800,224 . The biggest common factor number is the GCF number.
So the greatest common factor 800,224 is 32.

Lets's calculate LCM of 277,280

Lowest Common Multiple of 277,280 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 77560

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/77560

Therefore, the GCF of Fractions 800/277,224/280 is 32/77560

Least Common Multiple of 277,280 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 277,280 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(277,280) = 1

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

GCF(277,280) x common factors =1 x 1 = 1

LCM(277,280) = ( 277 × 280 ) / 1

LCM(277,280) = 77560 / 1

LCM(277,280) = 77560

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FAQs on GCF of Fractions of 800/277, 224/280

1. What is the HCF of 800,224?

The HCF of 800,224 is 32

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 800/277, 224/280?

Answer: GCF of Numerators as per given numbers 800/277, 224/280 is

GCF of Numerators i.e. for 800,224 is 32

LCM of denominators i.e. for 277,280 is 77560.

Thus, GCF of Fractions is 32/77560.Finally, GCF of Fractions for 800/277, 224/280 is 32/77560.