Greatest Common Factor of 67/27, 89/34, 306/102

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 67/27, 89/34, 306/102

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

Greatest Common Factor of 67/27,89/34,306/102

Given fractions are 67/27,89/34,306/102

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 67,89,306

Greatest Common Factor of Numerators i.e. GCF of 67,89,306 is 1 .

LCM of Denominators means LCM of 27,34,102 as per the given fractions.

LCM of 27,34,102 is 918 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 67,89,306

GCF of Fractions 67/27,89/34,306/102 is 1/918

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 67,89,306 By Matching Biggest Common Factor Method

Greatest Common Factor of 67,89,306 By Matching Biggest Common Factor Method

Factors of 67

List of positive integer factors of 67 that divides 67 without a remainder.

1,67

Factors of 89

List of positive integer factors of 89 that divides 89 without a remainder.

1,89

Factors of 306

List of positive integer factors of 306 that divides 306 without a remainder.

1,2,3,6,9,17,18,34,51,102,153,306

Greatest Common Factor

We found the factors 67,89,306 . The biggest common factor number is the GCF number.
So the greatest common factor 67,89,306 is 1.

Lets's calculate LCM of 27,34,102

2 27, 34, 102
3 27, 17, 51
17 9, 17, 17
9, 1, 1

∴ So the LCM of the given numbers is 2 x 3 x 17 x 9 x 1 x 1 = 918

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/918

Therefore, the GCF of Fractions 67/27,89/34,306/102 is 1/918

Least Common Multiple of 27,34,102 with GCF Formula

Least Common Multiple of 27,34,102 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 27,34,102 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(27,34,102) = 1

common factors(in case of two or more numbers have common factors) = 102

GCF(27,34,102) x common factors =1 x 102 = 102

LCM(27,34,102) = ( 27 × 34 × 102 ) / 102

LCM(27,34,102) = 93636 / 102

LCM(27,34,102) = 918


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 67/27, 89/34, 306/102

1. 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.

2. What is the GCF of Fractions for 67/27, 89/34, 306/102?

Answer: GCF of Numerators as per given numbers 67/27, 89/34, 306/102 is

GCF of Numerators i.e. for 67,89,306 is 1

LCM of denominators i.e. for 27,34,102 is 918.

Thus, GCF of Fractions is 1/918.Finally, GCF of Fractions for 67/27, 89/34, 306/102 is 1/918.