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GCF of 65/152, 7683/8512

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 65/152, 7683/8512 i.e 13/8512 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/152, 7683/8512.

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 65/152,7683/8512?

Given fractions are 65/152,7683/8512

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 65/152,7683/8512, numerators are 65,7683

Denominators are 152,8512

The GCF of 65,7683 is 13 .

LCM of 152,8512 is 8512.

The greatest common factor of 65/152,7683/8512 = [GCF of 65,7683]/[LCM of 152,8512]= 13/8512

Therefore, the GCF of 65/152,7683/8512 is 13/8512.

Greatest Common Factor of 65,7683

To find the highest common factor of 65,7683, we have to find the factors of both numbers and list the highest common factor.

The factors of 65 are 1, 5, 13, 65

The factors of 7683 are 1, 3, 13, 39, 197, 591, 2561, 7683

The HCF of 65,7683 is 13.

Lets's calculate GCF of 65,7683

Greatest Common Factor (GCF) of 65,7683 By Common Division

13 65, 7683
5, 591

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 65,7683 By Matching Biggest Common Factor Method

Greatest Common Factor of 65,7683 By Matching Biggest Common Factor Method

Now, list down the factors of 65

:

1,5,13,65

Now, list down the factors of 7683

:

1,3,13,39,197,591,2561,7683

Greatest Common Factor

We found the factors 65,7683 . The biggest common factor number is the GCF number.
So the greatest common factor 65,7683 is 13.

Lets's calculate LCM of 152,8512

Lowest Common Multiple of 152,8512 using Common Division

2 152, 8512
2 76, 4256
2 38, 2128
19 19, 1064
1, 56

∴ So the LCM of the given numbers is 2 x 2 x 2 x 19 x 1 x 56 = 8512

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/8512

Therefore, the GCF of Fractions 65/152,7683/8512 is 13/8512

Least Common Multiple of 152,8512 with GCF Formula

Least Common Multiple of 152,8512 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 152,8512 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(152,8512) = 152

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

GCF(152,8512) x common factors =152 x 1 = 152

LCM(152,8512) = ( 152 × 8512 ) / 152

LCM(152,8512) = 1293824 / 152

LCM(152,8512) = 8512


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FAQs on GCF of Fractions of 65/152, 7683/8512

1. What is the HCF of 65,7683?

The HCF of 65,7683 is 13

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 65/152, 7683/8512?

Answer: GCF of Numerators as per given numbers 65/152, 7683/8512 is

GCF of Numerators i.e. for 65,7683 is 13

LCM of denominators i.e. for 152,8512 is 8512.

Thus, GCF of Fractions is 13/8512.Finally, GCF of Fractions for 65/152, 7683/8512 is 13/8512.