How to Find GCF of 1614/410, 2322/841?

GCF of 1614/410, 2322/841

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 1614/410, 2322/841 i.e 6/344810 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1614/410, 2322/841.

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 1614/410,2322/841?

Given fractions are 1614/410,2322/841

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 1614/410,2322/841, numerators are 1614,2322

Denominators are 410,841

The GCF of 1614,2322 is 6 .

LCM of 410,841 is 344810.

The greatest common factor of 1614/410,2322/841 = [GCF of 1614,2322]/[LCM of 410,841]= 6/344810

Therefore, the GCF of 1614/410,2322/841 is 6/344810.

Greatest Common Factor of 1614,2322

To find the highest common factor of 1614,2322, we have to find the factors of both numbers and list the highest common factor.

The factors of 1614 are 1, 2, 3, 6, 269, 538, 807, 1614

The factors of 2322 are 1, 2, 3, 6, 9, 18, 27, 43, 54, 86, 129, 258, 387, 774, 1161, 2322

The HCF of 1614,2322 is 6.

Lets's calculate GCF of 1614,2322

Greatest Common Factor (GCF) of 1614,2322 By Common Division

2	1614, 2322
3	807, 1161
	269, 387

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 1614,2322 By Matching Biggest Common Factor Method

Now, list down the factors of 1614

1,2,3,6,269,538,807,1614

Now, list down the factors of 2322

1,2,3,6,9,18,27,43,54,86,129,258,387,774,1161,2322

Greatest Common Factor

We found the factors 1614,2322 . The biggest common factor number is the GCF number.
So the greatest common factor 1614,2322 is 6.

Lets's calculate LCM of 410,841

Lowest Common Multiple of 410,841 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 344810

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/344810

Therefore, the GCF of Fractions 1614/410,2322/841 is 6/344810

Least Common Multiple of 410,841 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 410,841 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(410,841) = 1

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

GCF(410,841) x common factors =1 x 1 = 1

LCM(410,841) = ( 410 × 841 ) / 1

LCM(410,841) = 344810 / 1

LCM(410,841) = 344810

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FAQs on GCF of Fractions of 1614/410, 2322/841

1. What is the HCF of 1614,2322?

The HCF of 1614,2322 is 6

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 1614/410, 2322/841?

Answer: GCF of Numerators as per given numbers 1614/410, 2322/841 is

GCF of Numerators i.e. for 1614,2322 is 6

LCM of denominators i.e. for 410,841 is 344810.

Thus, GCF of Fractions is 6/344810.Finally, GCF of Fractions for 1614/410, 2322/841 is 6/344810.