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GCF of 105/96, 765/943

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 105/96, 765/943 i.e 15/90528 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/96, 765/943.

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 105/96,765/943?

Given fractions are 105/96,765/943

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 105/96,765/943, numerators are 105,765

Denominators are 96,943

The GCF of 105,765 is 15 .

LCM of 96,943 is 90528.

The greatest common factor of 105/96,765/943 = [GCF of 105,765]/[LCM of 96,943]= 15/90528

Therefore, the GCF of 105/96,765/943 is 15/90528.

Greatest Common Factor of 105,765

To find the highest common factor of 105,765, 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 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765

The HCF of 105,765 is 15.

Lets's calculate GCF of 105,765

Greatest Common Factor (GCF) of 105,765 By Common Division

3 105, 765
5 35, 255
7, 51

∴ So the GCF of the given numbers is 3 x 5 = 15

Greatest Common Factor of 105,765 By Matching Biggest Common Factor Method

Greatest Common Factor of 105,765 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 765

:

1,3,5,9,15,17,45,51,85,153,255,765

Greatest Common Factor

We found the factors 105,765 . The biggest common factor number is the GCF number.
So the greatest common factor 105,765 is 15.


Lets's calculate LCM of 96,943

Lowest Common Multiple of 96,943 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 90528

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/90528

Therefore, the GCF of Fractions 105/96,765/943 is 15/90528

Least Common Multiple of 96,943 with GCF Formula

Least Common Multiple of 96,943 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 96,943 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(96,943) = 1

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

GCF(96,943) x common factors =1 x 1 = 1

LCM(96,943) = ( 96 × 943 ) / 1

LCM(96,943) = 90528 / 1

LCM(96,943) = 90528


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 105/96, 765/943

1. What is the HCF of 105,765?

The HCF of 105,765 is 15

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 105/96, 765/943?

Answer: GCF of Numerators as per given numbers 105/96, 765/943 is

GCF of Numerators i.e. for 105,765 is 15

LCM of denominators i.e. for 96,943 is 90528.

Thus, GCF of Fractions is 15/90528.Finally, GCF of Fractions for 105/96, 765/943 is 15/90528.