How to Find GCF of 2272/278, 6236/6853?

GCF of 2272/278, 6236/6853

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 2272/278, 6236/6853 i.e 4/1905134 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2272/278, 6236/6853.

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 2272/278,6236/6853?

Given fractions are 2272/278,6236/6853

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 2272/278,6236/6853, numerators are 2272,6236

Denominators are 278,6853

The GCF of 2272,6236 is 4 .

LCM of 278,6853 is 1905134.

The greatest common factor of 2272/278,6236/6853 = [GCF of 2272,6236]/[LCM of 278,6853]= 4/1905134

Therefore, the GCF of 2272/278,6236/6853 is 4/1905134.

Greatest Common Factor of 2272,6236

To find the highest common factor of 2272,6236, we have to find the factors of both numbers and list the highest common factor.

The factors of 2272 are 1, 2, 4, 8, 16, 32, 71, 142, 284, 568, 1136, 2272

The factors of 6236 are 1, 2, 4, 1559, 3118, 6236

The HCF of 2272,6236 is 4.

Lets's calculate GCF of 2272,6236

Greatest Common Factor (GCF) of 2272,6236 By Common Division

2	2272, 6236
2	1136, 3118
	568, 1559

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

Greatest Common Factor of 2272,6236 By Matching Biggest Common Factor Method

Now, list down the factors of 2272

1,2,4,8,16,32,71,142,284,568,1136,2272

Now, list down the factors of 6236

1,2,4,1559,3118,6236

Greatest Common Factor

We found the factors 2272,6236 . The biggest common factor number is the GCF number.
So the greatest common factor 2272,6236 is 4.

Lets's calculate LCM of 278,6853

Lowest Common Multiple of 278,6853 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1905134

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/1905134

Therefore, the GCF of Fractions 2272/278,6236/6853 is 4/1905134

Least Common Multiple of 278,6853 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 278,6853 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(278,6853) = 1

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

GCF(278,6853) x common factors =1 x 1 = 1

LCM(278,6853) = ( 278 × 6853 ) / 1

LCM(278,6853) = 1905134 / 1

LCM(278,6853) = 1905134

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FAQs on GCF of Fractions of 2272/278, 6236/6853

1. What is the HCF of 2272,6236?

The HCF of 2272,6236 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 2272/278, 6236/6853?

Answer: GCF of Numerators as per given numbers 2272/278, 6236/6853 is

GCF of Numerators i.e. for 2272,6236 is 4

LCM of denominators i.e. for 278,6853 is 1905134.

Thus, GCF of Fractions is 4/1905134.Finally, GCF of Fractions for 2272/278, 6236/6853 is 4/1905134.