How to Find GCF of 2266/308, 1188/416?

GCF of 2266/308, 1188/416

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 2266/308, 1188/416 i.e 22/32032 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2266/308, 1188/416.

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 2266/308,1188/416?

Given fractions are 2266/308,1188/416

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 2266/308,1188/416, numerators are 2266,1188

Denominators are 308,416

The GCF of 2266,1188 is 22 .

LCM of 308,416 is 32032.

The greatest common factor of 2266/308,1188/416 = [GCF of 2266,1188]/[LCM of 308,416]= 22/32032

Therefore, the GCF of 2266/308,1188/416 is 22/32032.

Greatest Common Factor of 2266,1188

To find the highest common factor of 2266,1188, we have to find the factors of both numbers and list the highest common factor.

The factors of 2266 are 1, 2, 11, 22, 103, 206, 1133, 2266

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 2266,1188 is 22.

Lets's calculate GCF of 2266,1188

Greatest Common Factor (GCF) of 2266,1188 By Common Division

2	2266, 1188
11	1133, 594
	103, 54

∴ So the GCF of the given numbers is 2 x 11 = 22

Greatest Common Factor of 2266,1188 By Matching Biggest Common Factor Method

Now, list down the factors of 2266

1,2,11,22,103,206,1133,2266

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 2266,1188 . The biggest common factor number is the GCF number.
So the greatest common factor 2266,1188 is 22.

Lets's calculate LCM of 308,416

Lowest Common Multiple of 308,416 using Common Division

2	308, 416
2	154, 208
	77, 104

∴ So the LCM of the given numbers is 2 x 2 x 77 x 104 = 32032

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/32032

Therefore, the GCF of Fractions 2266/308,1188/416 is 22/32032

Least Common Multiple of 308,416 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 308,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(308,416) = 4

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

GCF(308,416) x common factors =4 x 1 = 4

LCM(308,416) = ( 308 × 416 ) / 4

LCM(308,416) = 128128 / 4

LCM(308,416) = 32032

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FAQs on GCF of Fractions of 2266/308, 1188/416

1. What is the HCF of 2266,1188?

The HCF of 2266,1188 is 22

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 2266/308, 1188/416?

Answer: GCF of Numerators as per given numbers 2266/308, 1188/416 is

GCF of Numerators i.e. for 2266,1188 is 22

LCM of denominators i.e. for 308,416 is 32032.

Thus, GCF of Fractions is 22/32032.Finally, GCF of Fractions for 2266/308, 1188/416 is 22/32032.