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GCF of 105/30, 365/686

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 105/30, 365/686 i.e 5/10290 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/30, 365/686.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 105/30,365/686?

Given fractions are 105/30,365/686

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 105/30,365/686, numerators are 105,365

Denominators are 30,686

The GCF of 105,365 is 5 .

LCM of 30,686 is 10290.

The greatest common factor of 105/30,365/686 = [GCF of 105,365]/[LCM of 30,686]= 5/10290

Therefore, the GCF of 105/30,365/686 is 5/10290.

Greatest Common Factor of 105,365

To find the highest common factor of 105,365, we have to find the factors of both numbers and list the highest common factor.

The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105

The factors of 365 are 1, 5, 73, 365

The HCF of 105,365 is 5.

Lets's calculate GCF of 105,365

Greatest Common Factor (GCF) of 105,365 By Common Division

5 105, 365
21, 73

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 105,365 By Matching Biggest Common Factor Method

Greatest Common Factor of 105,365 By Matching Biggest Common Factor Method

Now, list down the factors of 105

:

1,3,5,7,15,21,35,105

Now, list down the factors of 365

:

1,5,73,365

Greatest Common Factor

We found the factors 105,365 . The biggest common factor number is the GCF number.
So the greatest common factor 105,365 is 5.

Lets's calculate LCM of 30,686

Lowest Common Multiple of 30,686 using Common Division

2 30, 686
15, 343

∴ So the LCM of the given numbers is 2 x 15 x 343 = 10290

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/10290

Therefore, the GCF of Fractions 105/30,365/686 is 5/10290

Least Common Multiple of 30,686 with GCF Formula

Least Common Multiple of 30,686 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 30,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,686) = 2

common factors(in case of two or more numbers have common factors) = 1

GCF(30,686) x common factors =2 x 1 = 2

LCM(30,686) = ( 30 × 686 ) / 2

LCM(30,686) = 20580 / 2

LCM(30,686) = 10290


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FAQs on GCF of Fractions of 105/30, 365/686

1. What is the HCF of 105,365?

The HCF of 105,365 is 5

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 105/30, 365/686?

Answer: GCF of Numerators as per given numbers 105/30, 365/686 is

GCF of Numerators i.e. for 105,365 is 5

LCM of denominators i.e. for 30,686 is 10290.

Thus, GCF of Fractions is 5/10290.Finally, GCF of Fractions for 105/30, 365/686 is 5/10290.