How to Find GCF of 40/188, 1386/6956?

GCF of 40/188, 1386/6956

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 40/188, 1386/6956 i.e 2/6956 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/188, 1386/6956.

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 40/188,1386/6956?

Given fractions are 40/188,1386/6956

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 40/188,1386/6956, numerators are 40,1386

Denominators are 188,6956

The GCF of 40,1386 is 2 .

LCM of 188,6956 is 6956.

The greatest common factor of 40/188,1386/6956 = [GCF of 40,1386]/[LCM of 188,6956]= 2/6956

Therefore, the GCF of 40/188,1386/6956 is 2/6956.

Greatest Common Factor of 40,1386

To find the highest common factor of 40,1386, we have to find the factors of both numbers and list the highest common factor.

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

The factors of 1386 are 1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 63, 66, 77, 99, 126, 154, 198, 231, 462, 693, 1386

The HCF of 40,1386 is 2.

Lets's calculate GCF of 40,1386

Greatest Common Factor (GCF) of 40,1386 By Common Division

2	40, 1386
	20, 693

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

Greatest Common Factor of 40,1386 By Matching Biggest Common Factor Method

Now, list down the factors of 40

1,2,4,5,8,10,20,40

Now, list down the factors of 1386

1,2,3,6,7,9,11,14,18,21,22,33,42,63,66,77,99,126,154,198,231,462,693,1386

Greatest Common Factor

We found the factors 40,1386 . The biggest common factor number is the GCF number.
So the greatest common factor 40,1386 is 2.

Lets's calculate LCM of 188,6956

Lowest Common Multiple of 188,6956 using Common Division

2	188, 6956
2	94, 3478
47	47, 1739
	1, 37

∴ So the LCM of the given numbers is 2 x 2 x 47 x 1 x 37 = 6956

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6956

Therefore, the GCF of Fractions 40/188,1386/6956 is 2/6956

Least Common Multiple of 188,6956 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 188,6956 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(188,6956) = 188

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

GCF(188,6956) x common factors =188 x 1 = 188

LCM(188,6956) = ( 188 × 6956 ) / 188

LCM(188,6956) = 1307728 / 188

LCM(188,6956) = 6956

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FAQs on GCF of Fractions of 40/188, 1386/6956

1. What is the HCF of 40,1386?

The HCF of 40,1386 is 2

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 40/188, 1386/6956?

Answer: GCF of Numerators as per given numbers 40/188, 1386/6956 is

GCF of Numerators i.e. for 40,1386 is 2

LCM of denominators i.e. for 188,6956 is 6956.

Thus, GCF of Fractions is 2/6956.Finally, GCF of Fractions for 40/188, 1386/6956 is 2/6956.