How to Find GCF of 512/682, 4305/1154?

GCF of 512/682, 4305/1154

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 512/682, 4305/1154 i.e 1/393514 easily. The following is the detailed procedure to determine the greatest common factor of fractions 512/682, 4305/1154.

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 512/682,4305/1154?

Given fractions are 512/682,4305/1154

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 512/682,4305/1154, numerators are 512,4305

Denominators are 682,1154

The GCF of 512,4305 is 1 .

LCM of 682,1154 is 393514.

The greatest common factor of 512/682,4305/1154 = [GCF of 512,4305]/[LCM of 682,1154]= 1/393514

Therefore, the GCF of 512/682,4305/1154 is 1/393514.

Greatest Common Factor of 512,4305

To find the highest common factor of 512,4305, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 4305 are 1, 3, 5, 7, 15, 21, 35, 41, 105, 123, 205, 287, 615, 861, 1435, 4305

The HCF of 512,4305 is 1.

Lets's calculate GCF of 512,4305

Greatest Common Factor (GCF) of 512,4305 By Common Division

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

Greatest Common Factor of 512,4305 By Matching Biggest Common Factor Method

Now, list down the factors of 512

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

Now, list down the factors of 4305

1,3,5,7,15,21,35,41,105,123,205,287,615,861,1435,4305

Greatest Common Factor

We found the factors 512,4305 . The biggest common factor number is the GCF number.
So the greatest common factor 512,4305 is 1.

Lets's calculate LCM of 682,1154

Lowest Common Multiple of 682,1154 using Common Division

2	682, 1154
	341, 577

∴ So the LCM of the given numbers is 2 x 341 x 577 = 393514

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/393514

Therefore, the GCF of Fractions 512/682,4305/1154 is 1/393514

Least Common Multiple of 682,1154 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 682,1154 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(682,1154) = 2

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

GCF(682,1154) x common factors =2 x 1 = 2

LCM(682,1154) = ( 682 × 1154 ) / 2

LCM(682,1154) = 787028 / 2

LCM(682,1154) = 393514

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FAQs on GCF of Fractions of 512/682, 4305/1154

1. What is the HCF of 512,4305?

The HCF of 512,4305 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 512/682, 4305/1154?

Answer: GCF of Numerators as per given numbers 512/682, 4305/1154 is

GCF of Numerators i.e. for 512,4305 is 1

LCM of denominators i.e. for 682,1154 is 393514.

Thus, GCF of Fractions is 1/393514.Finally, GCF of Fractions for 512/682, 4305/1154 is 1/393514.