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GCF of 287/312, 8769/960

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 287/312, 8769/960 i.e 1/12480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 287/312, 8769/960.

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 287/312,8769/960?

Given fractions are 287/312,8769/960

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 287/312,8769/960, numerators are 287,8769

Denominators are 312,960

The GCF of 287,8769 is 1 .

LCM of 312,960 is 12480.

The greatest common factor of 287/312,8769/960 = [GCF of 287,8769]/[LCM of 312,960]= 1/12480

Therefore, the GCF of 287/312,8769/960 is 1/12480.

Greatest Common Factor of 287,8769

To find the highest common factor of 287,8769, we have to find the factors of both numbers and list the highest common factor.

The factors of 287 are 1, 7, 41, 287

The factors of 8769 are 1, 3, 37, 79, 111, 237, 2923, 8769

The HCF of 287,8769 is 1.

Lets's calculate GCF of 287,8769

Greatest Common Factor (GCF) of 287,8769 By Common Division

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

Greatest Common Factor of 287,8769 By Matching Biggest Common Factor Method

Greatest Common Factor of 287,8769 By Matching Biggest Common Factor Method

Now, list down the factors of 287

:

1,7,41,287

Now, list down the factors of 8769

:

1,3,37,79,111,237,2923,8769

Greatest Common Factor

We found the factors 287,8769 . The biggest common factor number is the GCF number.
So the greatest common factor 287,8769 is 1.

Lets's calculate LCM of 312,960

Lowest Common Multiple of 312,960 using Common Division

2 312, 960
2 156, 480
2 78, 240
3 39, 120
13, 40

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 13 x 40 = 12480

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12480

Therefore, the GCF of Fractions 287/312,8769/960 is 1/12480

Least Common Multiple of 312,960 with GCF Formula

Least Common Multiple of 312,960 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 312,960 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(312,960) = 24

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

GCF(312,960) x common factors =24 x 1 = 24

LCM(312,960) = ( 312 × 960 ) / 24

LCM(312,960) = 299520 / 24

LCM(312,960) = 12480


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FAQs on GCF of Fractions of 287/312, 8769/960

1. What is the HCF of 287,8769?

The HCF of 287,8769 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 287/312, 8769/960?

Answer: GCF of Numerators as per given numbers 287/312, 8769/960 is

GCF of Numerators i.e. for 287,8769 is 1

LCM of denominators i.e. for 312,960 is 12480.

Thus, GCF of Fractions is 1/12480.Finally, GCF of Fractions for 287/312, 8769/960 is 1/12480.