How to Find GCF of 280/985, 200/822?

GCF of 280/985, 200/822

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 280/985, 200/822 i.e 40/809670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 280/985, 200/822.

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 280/985,200/822?

Given fractions are 280/985,200/822

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 280/985,200/822, numerators are 280,200

Denominators are 985,822

The GCF of 280,200 is 40 .

LCM of 985,822 is 809670.

The greatest common factor of 280/985,200/822 = [GCF of 280,200]/[LCM of 985,822]= 40/809670

Therefore, the GCF of 280/985,200/822 is 40/809670.

Greatest Common Factor of 280,200

To find the highest common factor of 280,200, we have to find the factors of both numbers and list the highest common factor.

The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280

The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

The HCF of 280,200 is 40.

Lets's calculate GCF of 280,200

Greatest Common Factor (GCF) of 280,200 By Common Division

2	280, 200
2	140, 100
2	70, 50
5	35, 25
	7, 5

∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40

Greatest Common Factor of 280,200 By Matching Biggest Common Factor Method

Now, list down the factors of 280

1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280

Now, list down the factors of 200

1,2,4,5,8,10,20,25,40,50,100,200

Greatest Common Factor

We found the factors 280,200 . The biggest common factor number is the GCF number.
So the greatest common factor 280,200 is 40.

Lets's calculate LCM of 985,822

Lowest Common Multiple of 985,822 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 809670

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/809670

Therefore, the GCF of Fractions 280/985,200/822 is 40/809670

Least Common Multiple of 985,822 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 985,822 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(985,822) = 1

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

GCF(985,822) x common factors =1 x 1 = 1

LCM(985,822) = ( 985 × 822 ) / 1

LCM(985,822) = 809670 / 1

LCM(985,822) = 809670

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FAQs on GCF of Fractions of 280/985, 200/822

1. What is the HCF of 280,200?

The HCF of 280,200 is 40

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 280/985, 200/822?

Answer: GCF of Numerators as per given numbers 280/985, 200/822 is

GCF of Numerators i.e. for 280,200 is 40

LCM of denominators i.e. for 985,822 is 809670.

Thus, GCF of Fractions is 40/809670.Finally, GCF of Fractions for 280/985, 200/822 is 40/809670.