How to Find GCF of 685/23, 703/65, 512/13?

GCF of 685/23, 703/65, 512/13

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 685/23, 703/65, 512/13 i.e 1/1495 easily. The following is the detailed procedure to determine the greatest common factor of fractions 685/23, 703/65, 512/13.

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 685/23,703/65,512/13?

Given fractions are 685/23,703/65,512/13

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 685/23,703/65,512/13, numerators are 685,703,512

Denominators are 23,65,13

The GCF of 685,703,512 is 1 .

LCM of 23,65,13 is 1495.

The greatest common factor of 685/23,703/65,512/13 = [GCF of 685,703,512]/[LCM of 23,65,13]= 1/1495

Therefore, the GCF of 685/23,703/65,512/13 is 1/1495.

Greatest Common Factor of 685,703,512

To find the highest common factor of 685,703,512, we have to find the factors of both numbers and list the highest common factor.

The factors of 685 are 1, 5, 137, 685

The factors of 703 are 1, 19, 37, 703

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The HCF of 685,703,512 is 1.

Lets's calculate GCF of 685,703,512

Greatest Common Factor (GCF) of 685,703,512 By Common Division

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

Greatest Common Factor of 685,703,512 By Matching Biggest Common Factor Method

Now, list down the factors of 685

1,5,137,685

Now, list down the factors of 703

1,19,37,703

Now, list down the factors of 512

1,2,4,8,16,32,64,128,256,512

Greatest Common Factor

We found the factors 685,703,512 . The biggest common factor number is the GCF number.
So the greatest common factor 685,703,512 is 1.

Lets's calculate LCM of 23,65,13

Lowest Common Multiple of 23,65,13 using Common Division

13	23, 65, 13
	23, 5, 1

∴ So the LCM of the given numbers is 13 x 23 x 5 x 1 = 1495

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1495

Therefore, the GCF of Fractions 685/23,703/65,512/13 is 1/1495

Least Common Multiple of 23,65,13 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 23,65,13 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,65,13) = 1

common factors(in case of two or more numbers have common factors) = 13

GCF(23,65,13) x common factors =1 x 13 = 13

LCM(23,65,13) = ( 23 × 65 × 13 ) / 13

LCM(23,65,13) = 19435 / 13

LCM(23,65,13) = 1495

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 685/23, 703/65, 512/13

1. What is the HCF of 685,703,512?

The HCF of 685,703,512 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 685/23, 703/65, 512/13?

Answer: GCF of Numerators as per given numbers 685/23, 703/65, 512/13 is

GCF of Numerators i.e. for 685,703,512 is 1

LCM of denominators i.e. for 23,65,13 is 1495.

Thus, GCF of Fractions is 1/1495.Finally, GCF of Fractions for 685/23, 703/65, 512/13 is 1/1495.