How to Find GCF of 30/32, 68/66, 310/766?

GCF of 30/32, 68/66, 310/766

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 30/32, 68/66, 310/766 i.e 2/404448 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/32, 68/66, 310/766.

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 30/32,68/66,310/766?

Given fractions are 30/32,68/66,310/766

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 30/32,68/66,310/766, numerators are 30,68,310

Denominators are 32,66,766

The GCF of 30,68,310 is 2 .

LCM of 32,66,766 is 404448.

The greatest common factor of 30/32,68/66,310/766 = [GCF of 30,68,310]/[LCM of 32,66,766]= 2/404448

Therefore, the GCF of 30/32,68/66,310/766 is 2/404448.

Greatest Common Factor of 30,68,310

To find the highest common factor of 30,68,310, we have to find the factors of both numbers and list the highest common factor.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

The factors of 68 are 1, 2, 4, 17, 34, 68

The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310

The HCF of 30,68,310 is 2.

Lets's calculate GCF of 30,68,310

Greatest Common Factor (GCF) of 30,68,310 By Common Division

2	30, 68, 310
	15, 34, 155

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

Greatest Common Factor of 30,68,310 By Matching Biggest Common Factor Method

Now, list down the factors of 30

1,2,3,5,6,10,15,30

Now, list down the factors of 68

1,2,4,17,34,68

Now, list down the factors of 310

1,2,5,10,31,62,155,310

Greatest Common Factor

We found the factors 30,68,310 . The biggest common factor number is the GCF number.
So the greatest common factor 30,68,310 is 2.

Lets's calculate LCM of 32,66,766

Lowest Common Multiple of 32,66,766 using Common Division

2	32, 66, 766
	16, 33, 383

∴ So the LCM of the given numbers is 2 x 16 x 33 x 383 = 404448

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/404448

Therefore, the GCF of Fractions 30/32,68/66,310/766 is 2/404448

Least Common Multiple of 32,66,766 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 32,66,766 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(32,66,766) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(32,66,766) x common factors =2 x 2 = 4

LCM(32,66,766) = ( 32 × 66 × 766 ) / 4

LCM(32,66,766) = 1617792 / 4

LCM(32,66,766) = 404448

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 30/32, 68/66, 310/766

1. What is the HCF of 30,68,310?

The HCF of 30,68,310 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 30/32, 68/66, 310/766?

Answer: GCF of Numerators as per given numbers 30/32, 68/66, 310/766 is

GCF of Numerators i.e. for 30,68,310 is 2

LCM of denominators i.e. for 32,66,766 is 404448.

Thus, GCF of Fractions is 2/404448.Finally, GCF of Fractions for 30/32, 68/66, 310/766 is 2/404448.