How to Find GCF of 10/67, 512/82, 321/109?

GCF of 10/67, 512/82, 321/109

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 10/67, 512/82, 321/109 i.e 1/598846 easily. The following is the detailed procedure to determine the greatest common factor of fractions 10/67, 512/82, 321/109.

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 10/67,512/82,321/109?

Given fractions are 10/67,512/82,321/109

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 10/67,512/82,321/109, numerators are 10,512,321

Denominators are 67,82,109

The GCF of 10,512,321 is 1 .

LCM of 67,82,109 is 598846.

The greatest common factor of 10/67,512/82,321/109 = [GCF of 10,512,321]/[LCM of 67,82,109]= 1/598846

Therefore, the GCF of 10/67,512/82,321/109 is 1/598846.

Greatest Common Factor of 10,512,321

To find the highest common factor of 10,512,321, we have to find the factors of both numbers and list the highest common factor.

The factors of 10 are 1, 2, 5, 10

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

The factors of 321 are 1, 3, 107, 321

The HCF of 10,512,321 is 1.

Lets's calculate GCF of 10,512,321

Greatest Common Factor (GCF) of 10,512,321 By Common Division

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

Greatest Common Factor of 10,512,321 By Matching Biggest Common Factor Method

Now, list down the factors of 10

1,2,5,10

Now, list down the factors of 512

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

Now, list down the factors of 321

1,3,107,321

Greatest Common Factor

We found the factors 10,512,321 . The biggest common factor number is the GCF number.
So the greatest common factor 10,512,321 is 1.

Lets's calculate LCM of 67,82,109

Lowest Common Multiple of 67,82,109 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 598846

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/598846

Therefore, the GCF of Fractions 10/67,512/82,321/109 is 1/598846

Least Common Multiple of 67,82,109 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 67,82,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(67,82,109) = 1

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

GCF(67,82,109) x common factors =1 x 1 = 1

LCM(67,82,109) = ( 67 × 82 × 109 ) / 1

LCM(67,82,109) = 598846 / 1

LCM(67,82,109) = 598846

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FAQs on GCF of Fractions of 10/67, 512/82, 321/109

1. What is the HCF of 10,512,321?

The HCF of 10,512,321 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 10/67, 512/82, 321/109?

Answer: GCF of Numerators as per given numbers 10/67, 512/82, 321/109 is

GCF of Numerators i.e. for 10,512,321 is 1

LCM of denominators i.e. for 67,82,109 is 598846.

Thus, GCF of Fractions is 1/598846.Finally, GCF of Fractions for 10/67, 512/82, 321/109 is 1/598846.