How to Find GCF of 188/446, 312/508?

GCF of 188/446, 312/508

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 188/446, 312/508 i.e 4/113284 easily. The following is the detailed procedure to determine the greatest common factor of fractions 188/446, 312/508.

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 188/446,312/508?

Given fractions are 188/446,312/508

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 188/446,312/508, numerators are 188,312

Denominators are 446,508

The GCF of 188,312 is 4 .

LCM of 446,508 is 113284.

The greatest common factor of 188/446,312/508 = [GCF of 188,312]/[LCM of 446,508]= 4/113284

Therefore, the GCF of 188/446,312/508 is 4/113284.

Greatest Common Factor of 188,312

To find the highest common factor of 188,312, we have to find the factors of both numbers and list the highest common factor.

The factors of 188 are 1, 2, 4, 47, 94, 188

The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

The HCF of 188,312 is 4.

Lets's calculate GCF of 188,312

Greatest Common Factor (GCF) of 188,312 By Common Division

2	188, 312
2	94, 156
	47, 78

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

Greatest Common Factor of 188,312 By Matching Biggest Common Factor Method

Now, list down the factors of 188

1,2,4,47,94,188

Now, list down the factors of 312

1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312

Greatest Common Factor

We found the factors 188,312 . The biggest common factor number is the GCF number.
So the greatest common factor 188,312 is 4.

Lets's calculate LCM of 446,508

Lowest Common Multiple of 446,508 using Common Division

2	446, 508
	223, 254

∴ So the LCM of the given numbers is 2 x 223 x 254 = 113284

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/113284

Therefore, the GCF of Fractions 188/446,312/508 is 4/113284

Least Common Multiple of 446,508 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 446,508 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(446,508) = 2

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

GCF(446,508) x common factors =2 x 1 = 2

LCM(446,508) = ( 446 × 508 ) / 2

LCM(446,508) = 226568 / 2

LCM(446,508) = 113284

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FAQs on GCF of Fractions of 188/446, 312/508

1. What is the HCF of 188,312?

The HCF of 188,312 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 188/446, 312/508?

Answer: GCF of Numerators as per given numbers 188/446, 312/508 is

GCF of Numerators i.e. for 188,312 is 4

LCM of denominators i.e. for 446,508 is 113284.

Thus, GCF of Fractions is 4/113284.Finally, GCF of Fractions for 188/446, 312/508 is 4/113284.