Greatest Common Factor of 76/70, 66/45, 40/21, 45/84

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 76/70, 66/45, 40/21, 45/84

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 76/70,66/45,40/21,45/84

Given fractions are 76/70,66/45,40/21,45/84

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 76,66,40,45

Greatest Common Factor of Numerators i.e. GCF of 76,66,40,45 is 1 .

LCM of Denominators means LCM of 70,45,21,84 as per the given fractions.

LCM of 70,45,21,84 is 1260 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 76,66,40,45

GCF of Fractions 76/70,66/45,40/21,45/84 is 1/1260

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

Greatest Common Factor of 76,66,40,45 By Matching Biggest Common Factor Method

Greatest Common Factor of 76,66,40,45 By Matching Biggest Common Factor Method

Factors of 76

List of positive integer factors of 76 that divides 76 without a remainder.

1,2,4,19,38,76

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 40

List of positive integer factors of 40 that divides 40 without a remainder.

1,2,4,5,8,10,20,40

Factors of 45

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

1,3,5,9,15,45

Greatest Common Factor

We found the factors 76,66,40,45 . The biggest common factor number is the GCF number.
So the greatest common factor 76,66,40,45 is 1.

Lets's calculate LCM of 70,45,21,84

2 70, 45, 21, 84
3 35, 45, 21, 42
5 35, 15, 7, 14
7 7, 3, 7, 14
1, 3, 1, 2

∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 1 x 3 x 1 x 2 = 1260

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1260

Therefore, the GCF of Fractions 76/70,66/45,40/21,45/84 is 1/1260

Least Common Multiple of 70,45,21,84 with GCF Formula

Least Common Multiple of 70,45,21,84 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 70,45,21,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(70,45,21,84) = 1

common factors(in case of two or more numbers have common factors) = 4410

GCF(70,45,21,84) x common factors =1 x 4410 = 4410

LCM(70,45,21,84) = ( 70 × 45 × 21 × 84 ) / 4410

LCM(70,45,21,84) = 5556600 / 4410

LCM(70,45,21,84) = 1260


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 76/70, 66/45, 40/21, 45/84

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 76/70, 66/45, 40/21, 45/84?

Answer: GCF of Numerators as per given numbers 76/70, 66/45, 40/21, 45/84 is

GCF of Numerators i.e. for 76,66,40,45 is 1

LCM of denominators i.e. for 70,45,21,84 is 1260.

Thus, GCF of Fractions is 1/1260.Finally, GCF of Fractions for 76/70, 66/45, 40/21, 45/84 is 1/1260.