How to Find GCF of 6782/234, 2417/2478?

GCF of 6782/234, 2417/2478

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 6782/234, 2417/2478 i.e 1/96642 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6782/234, 2417/2478.

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 6782/234,2417/2478?

Given fractions are 6782/234,2417/2478

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 6782/234,2417/2478, numerators are 6782,2417

Denominators are 234,2478

The GCF of 6782,2417 is 1 .

LCM of 234,2478 is 96642.

The greatest common factor of 6782/234,2417/2478 = [GCF of 6782,2417]/[LCM of 234,2478]= 1/96642

Therefore, the GCF of 6782/234,2417/2478 is 1/96642.

Greatest Common Factor of 6782,2417

To find the highest common factor of 6782,2417, we have to find the factors of both numbers and list the highest common factor.

The factors of 6782 are 1, 2, 3391, 6782

The factors of 2417 are 1, 2417

The HCF of 6782,2417 is 1.

Lets's calculate GCF of 6782,2417

Greatest Common Factor (GCF) of 6782,2417 By Common Division

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

Greatest Common Factor of 6782,2417 By Matching Biggest Common Factor Method

Now, list down the factors of 6782

1,2,3391,6782

Now, list down the factors of 2417

1,2417

Greatest Common Factor

We found the factors 6782,2417 . The biggest common factor number is the GCF number.
So the greatest common factor 6782,2417 is 1.

Lets's calculate LCM of 234,2478

Lowest Common Multiple of 234,2478 using Common Division

2	234, 2478
3	117, 1239
	39, 413

∴ So the LCM of the given numbers is 2 x 3 x 39 x 413 = 96642

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/96642

Therefore, the GCF of Fractions 6782/234,2417/2478 is 1/96642

Least Common Multiple of 234,2478 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 234,2478 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(234,2478) = 6

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

GCF(234,2478) x common factors =6 x 1 = 6

LCM(234,2478) = ( 234 × 2478 ) / 6

LCM(234,2478) = 579852 / 6

LCM(234,2478) = 96642

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FAQs on GCF of Fractions of 6782/234, 2417/2478

1. What is the HCF of 6782,2417?

The HCF of 6782,2417 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 6782/234, 2417/2478?

Answer: GCF of Numerators as per given numbers 6782/234, 2417/2478 is

GCF of Numerators i.e. for 6782,2417 is 1

LCM of denominators i.e. for 234,2478 is 96642.

Thus, GCF of Fractions is 1/96642.Finally, GCF of Fractions for 6782/234, 2417/2478 is 1/96642.