How to Find GCF of 32/314, 20/691, 222/655?

GCF of 32/314, 20/691, 222/655

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 32/314, 20/691, 222/655 i.e 2/142117970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 32/314, 20/691, 222/655.

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 32/314,20/691,222/655?

Given fractions are 32/314,20/691,222/655

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 32/314,20/691,222/655, numerators are 32,20,222

Denominators are 314,691,655

The GCF of 32,20,222 is 2 .

LCM of 314,691,655 is 142117970.

The greatest common factor of 32/314,20/691,222/655 = [GCF of 32,20,222]/[LCM of 314,691,655]= 2/142117970

Therefore, the GCF of 32/314,20/691,222/655 is 2/142117970.

Greatest Common Factor of 32,20,222

To find the highest common factor of 32,20,222, we have to find the factors of both numbers and list the highest common factor.

The factors of 32 are 1, 2, 4, 8, 16, 32

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

The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222

The HCF of 32,20,222 is 2.

Lets's calculate GCF of 32,20,222

Greatest Common Factor (GCF) of 32,20,222 By Common Division

2	32, 20, 222
	16, 10, 111

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

Greatest Common Factor of 32,20,222 By Matching Biggest Common Factor Method

Now, list down the factors of 32

1,2,4,8,16,32

Now, list down the factors of 20

1,2,4,5,10,20

Now, list down the factors of 222

1,2,3,6,37,74,111,222

Greatest Common Factor

We found the factors 32,20,222 . The biggest common factor number is the GCF number.
So the greatest common factor 32,20,222 is 2.

Lets's calculate LCM of 314,691,655

Lowest Common Multiple of 314,691,655 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 142117970

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/142117970

Therefore, the GCF of Fractions 32/314,20/691,222/655 is 2/142117970

Least Common Multiple of 314,691,655 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 314,691,655 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,691,655) = 1

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

GCF(314,691,655) x common factors =1 x 1 = 1

LCM(314,691,655) = ( 314 × 691 × 655 ) / 1

LCM(314,691,655) = 142117970 / 1

LCM(314,691,655) = 142117970

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 32/314, 20/691, 222/655

1. What is the HCF of 32,20,222?

The HCF of 32,20,222 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 32/314, 20/691, 222/655?

Answer: GCF of Numerators as per given numbers 32/314, 20/691, 222/655 is

GCF of Numerators i.e. for 32,20,222 is 2

LCM of denominators i.e. for 314,691,655 is 142117970.

Thus, GCF of Fractions is 2/142117970.Finally, GCF of Fractions for 32/314, 20/691, 222/655 is 2/142117970.