How to Find GCF of 224/421, 1188/892?

GCF of 224/421, 1188/892

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 224/421, 1188/892 i.e 4/375532 easily. The following is the detailed procedure to determine the greatest common factor of fractions 224/421, 1188/892.

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 224/421,1188/892?

Given fractions are 224/421,1188/892

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 224/421,1188/892, numerators are 224,1188

Denominators are 421,892

The GCF of 224,1188 is 4 .

LCM of 421,892 is 375532.

The greatest common factor of 224/421,1188/892 = [GCF of 224,1188]/[LCM of 421,892]= 4/375532

Therefore, the GCF of 224/421,1188/892 is 4/375532.

Greatest Common Factor of 224,1188

To find the highest common factor of 224,1188, 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 1188 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 99, 108, 132, 198, 297, 396, 594, 1188

The HCF of 224,1188 is 4.

Lets's calculate GCF of 224,1188

Greatest Common Factor (GCF) of 224,1188 By Common Division

2	224, 1188
2	112, 594
	56, 297

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 224,1188 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 1188

1,2,3,4,6,9,11,12,18,22,27,33,36,44,54,66,99,108,132,198,297,396,594,1188

Greatest Common Factor

We found the factors 224,1188 . The biggest common factor number is the GCF number.
So the greatest common factor 224,1188 is 4.

Lets's calculate LCM of 421,892

Lowest Common Multiple of 421,892 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 375532

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/375532

Therefore, the GCF of Fractions 224/421,1188/892 is 4/375532

Least Common Multiple of 421,892 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 421,892 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(421,892) = 1

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

GCF(421,892) x common factors =1 x 1 = 1

LCM(421,892) = ( 421 × 892 ) / 1

LCM(421,892) = 375532 / 1

LCM(421,892) = 375532

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FAQs on GCF of Fractions of 224/421, 1188/892

1. What is the HCF of 224,1188?

The HCF of 224,1188 is 4

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 224/421, 1188/892?

Answer: GCF of Numerators as per given numbers 224/421, 1188/892 is

GCF of Numerators i.e. for 224,1188 is 4

LCM of denominators i.e. for 421,892 is 375532.

Thus, GCF of Fractions is 4/375532.Finally, GCF of Fractions for 224/421, 1188/892 is 4/375532.