How to Find GCF of 45/586, 77/684, 406/365?

GCF of 45/586, 77/684, 406/365

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 45/586, 77/684, 406/365 i.e 1/73150380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 45/586, 77/684, 406/365.

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 45/586,77/684,406/365?

Given fractions are 45/586,77/684,406/365

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 45/586,77/684,406/365, numerators are 45,77,406

Denominators are 586,684,365

The GCF of 45,77,406 is 1 .

LCM of 586,684,365 is 73150380.

The greatest common factor of 45/586,77/684,406/365 = [GCF of 45,77,406]/[LCM of 586,684,365]= 1/73150380

Therefore, the GCF of 45/586,77/684,406/365 is 1/73150380.

Greatest Common Factor of 45,77,406

To find the highest common factor of 45,77,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 45 are 1, 3, 5, 9, 15, 45

The factors of 77 are 1, 7, 11, 77

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 45,77,406 is 1.

Lets's calculate GCF of 45,77,406

Greatest Common Factor (GCF) of 45,77,406 By Common Division

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

Greatest Common Factor of 45,77,406 By Matching Biggest Common Factor Method

Now, list down the factors of 45

1,3,5,9,15,45

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 406

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 45,77,406 . The biggest common factor number is the GCF number.
So the greatest common factor 45,77,406 is 1.

Lets's calculate LCM of 586,684,365

Lowest Common Multiple of 586,684,365 using Common Division

2	586, 684, 365
	293, 342, 365

∴ So the LCM of the given numbers is 2 x 293 x 342 x 365 = 73150380

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/73150380

Therefore, the GCF of Fractions 45/586,77/684,406/365 is 1/73150380

Least Common Multiple of 586,684,365 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 586,684,365 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(586,684,365) = 1

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

GCF(586,684,365) x common factors =1 x 2 = 2

LCM(586,684,365) = ( 586 × 684 × 365 ) / 2

LCM(586,684,365) = 146300760 / 2

LCM(586,684,365) = 73150380

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 45/586, 77/684, 406/365

1. What is the HCF of 45,77,406?

The HCF of 45,77,406 is 1

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 45/586, 77/684, 406/365?

Answer: GCF of Numerators as per given numbers 45/586, 77/684, 406/365 is

GCF of Numerators i.e. for 45,77,406 is 1

LCM of denominators i.e. for 586,684,365 is 73150380.

Thus, GCF of Fractions is 1/73150380.Finally, GCF of Fractions for 45/586, 77/684, 406/365 is 1/73150380.