How to Find GCF of 224/72, 800/674?

GCF of 224/72, 800/674

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 224/72, 800/674 i.e 32/24264 easily. The following is the detailed procedure to determine the greatest common factor of fractions 224/72, 800/674.

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 224/72,800/674?

Given fractions are 224/72,800/674

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 224/72,800/674, numerators are 224,800

Denominators are 72,674

The GCF of 224,800 is 32 .

LCM of 72,674 is 24264.

The greatest common factor of 224/72,800/674 = [GCF of 224,800]/[LCM of 72,674]= 32/24264

Therefore, the GCF of 224/72,800/674 is 32/24264.

Greatest Common Factor of 224,800

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

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

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

The HCF of 224,800 is 32.

Lets's calculate GCF of 224,800

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

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

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

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

Now, list down the factors of 224

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

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

Greatest Common Factor

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

Lets's calculate LCM of 72,674

Lowest Common Multiple of 72,674 using Common Division

2	72, 674
	36, 337

∴ So the LCM of the given numbers is 2 x 36 x 337 = 24264

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/24264

Therefore, the GCF of Fractions 224/72,800/674 is 32/24264

Least Common Multiple of 72,674 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 72,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(72,674) = 2

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

GCF(72,674) x common factors =2 x 1 = 2

LCM(72,674) = ( 72 × 674 ) / 2

LCM(72,674) = 48528 / 2

LCM(72,674) = 24264

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FAQs on GCF of Fractions of 224/72, 800/674

1. What is the HCF of 224,800?

The HCF of 224,800 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 224/72, 800/674?

Answer: GCF of Numerators as per given numbers 224/72, 800/674 is

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

LCM of denominators i.e. for 72,674 is 24264.

Thus, GCF of Fractions is 32/24264.Finally, GCF of Fractions for 224/72, 800/674 is 32/24264.