Greatest Common Factor of 61/34, 34/49, 45/30, 21/506

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 61/34, 34/49, 45/30, 21/506

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 61/34,34/49,45/30,21/506

Given fractions are 61/34,34/49,45/30,21/506

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 61,34,45,21

Greatest Common Factor of Numerators i.e. GCF of 61,34,45,21 is 1 .

LCM of Denominators means LCM of 34,49,30,506 as per the given fractions.

LCM of 34,49,30,506 is 6322470 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 61,34,45,21

GCF of Fractions 61/34,34/49,45/30,21/506 is 1/6322470

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

Greatest Common Factor of 61,34,45,21 By Matching Biggest Common Factor Method

Greatest Common Factor of 61,34,45,21 By Matching Biggest Common Factor Method

Factors of 61

List of positive integer factors of 61 that divides 61 without a remainder.

1,61

Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1,2,17,34

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

Greatest Common Factor

We found the factors 61,34,45,21 . The biggest common factor number is the GCF number.
So the greatest common factor 61,34,45,21 is 1.

Lets's calculate LCM of 34,49,30,506

2 34, 49, 30, 506
17, 49, 15, 253

∴ So the LCM of the given numbers is 2 x 17 x 49 x 15 x 253 = 6322470

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6322470

Therefore, the GCF of Fractions 61/34,34/49,45/30,21/506 is 1/6322470

Least Common Multiple of 34,49,30,506 with GCF Formula

Least Common Multiple of 34,49,30,506 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 34,49,30,506 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,49,30,506) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(34,49,30,506) x common factors =1 x 4 = 4

LCM(34,49,30,506) = ( 34 × 49 × 30 × 506 ) / 4

LCM(34,49,30,506) = 25289880 / 4

LCM(34,49,30,506) = 6322470


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 61/34, 34/49, 45/30, 21/506

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 61/34, 34/49, 45/30, 21/506?

Answer: GCF of Numerators as per given numbers 61/34, 34/49, 45/30, 21/506 is

GCF of Numerators i.e. for 61,34,45,21 is 1

LCM of denominators i.e. for 34,49,30,506 is 6322470.

Thus, GCF of Fractions is 1/6322470.Finally, GCF of Fractions for 61/34, 34/49, 45/30, 21/506 is 1/6322470.