Greatest Common Factor of 85/70, 66/22, 31/42, 729/30

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 85/70, 66/22, 31/42, 729/30

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 85/70,66/22,31/42,729/30

Given fractions are 85/70,66/22,31/42,729/30

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 85,66,31,729

Greatest Common Factor of Numerators i.e. GCF of 85,66,31,729 is 1 .

LCM of Denominators means LCM of 70,22,42,30 as per the given fractions.

LCM of 70,22,42,30 is 2310 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 85,66,31,729

GCF of Fractions 85/70,66/22,31/42,729/30 is 1/2310

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

Greatest Common Factor of 85,66,31,729 By Matching Biggest Common Factor Method

Greatest Common Factor of 85,66,31,729 By Matching Biggest Common Factor Method

Factors of 85

List of positive integer factors of 85 that divides 85 without a remainder.

1,5,17,85

Factors of 66

List of positive integer factors of 66 that divides 66 without a remainder.

1,2,3,6,11,22,33,66

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1,31

Factors of 729

List of positive integer factors of 729 that divides 729 without a remainder.

1,3,9,27,81,243,729

Greatest Common Factor

We found the factors 85,66,31,729 . The biggest common factor number is the GCF number.
So the greatest common factor 85,66,31,729 is 1.

Lets's calculate LCM of 70,22,42,30

2 70, 22, 42, 30
3 35, 11, 21, 15
5 35, 11, 7, 5
7 7, 11, 7, 1
1, 11, 1, 1

∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 1 x 11 x 1 x 1 = 2310

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2310

Therefore, the GCF of Fractions 85/70,66/22,31/42,729/30 is 1/2310

Least Common Multiple of 70,22,42,30 with GCF Formula

Least Common Multiple of 70,22,42,30 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 70,22,42,30 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(70,22,42,30) = 2

common factors(in case of two or more numbers have common factors) = 420

GCF(70,22,42,30) x common factors =2 x 420 = 840

LCM(70,22,42,30) = ( 70 × 22 × 42 × 30 ) / 840

LCM(70,22,42,30) = 1940400 / 840

LCM(70,22,42,30) = 2310


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 85/70, 66/22, 31/42, 729/30

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 85/70, 66/22, 31/42, 729/30?

Answer: GCF of Numerators as per given numbers 85/70, 66/22, 31/42, 729/30 is

GCF of Numerators i.e. for 85,66,31,729 is 1

LCM of denominators i.e. for 70,22,42,30 is 2310.

Thus, GCF of Fractions is 1/2310.Finally, GCF of Fractions for 85/70, 66/22, 31/42, 729/30 is 1/2310.