How to Find GCF of 3413/684, 6721/1040?

GCF of 3413/684, 6721/1040

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 3413/684, 6721/1040 i.e 1/177840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3413/684, 6721/1040.

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 3413/684,6721/1040?

Given fractions are 3413/684,6721/1040

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 3413/684,6721/1040, numerators are 3413,6721

Denominators are 684,1040

The GCF of 3413,6721 is 1 .

LCM of 684,1040 is 177840.

The greatest common factor of 3413/684,6721/1040 = [GCF of 3413,6721]/[LCM of 684,1040]= 1/177840

Therefore, the GCF of 3413/684,6721/1040 is 1/177840.

Greatest Common Factor of 3413,6721

To find the highest common factor of 3413,6721, we have to find the factors of both numbers and list the highest common factor.

The factors of 3413 are 1, 3413

The factors of 6721 are 1, 11, 13, 47, 143, 517, 611, 6721

The HCF of 3413,6721 is 1.

Lets's calculate GCF of 3413,6721

Greatest Common Factor (GCF) of 3413,6721 By Common Division

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

Greatest Common Factor of 3413,6721 By Matching Biggest Common Factor Method

Now, list down the factors of 3413

1,3413

Now, list down the factors of 6721

1,11,13,47,143,517,611,6721

Greatest Common Factor

We found the factors 3413,6721 . The biggest common factor number is the GCF number.
So the greatest common factor 3413,6721 is 1.

Lets's calculate LCM of 684,1040

Lowest Common Multiple of 684,1040 using Common Division

2	684, 1040
2	342, 520
	171, 260

∴ So the LCM of the given numbers is 2 x 2 x 171 x 260 = 177840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/177840

Therefore, the GCF of Fractions 3413/684,6721/1040 is 1/177840

Least Common Multiple of 684,1040 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 684,1040 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(684,1040) = 4

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

GCF(684,1040) x common factors =4 x 1 = 4

LCM(684,1040) = ( 684 × 1040 ) / 4

LCM(684,1040) = 711360 / 4

LCM(684,1040) = 177840

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 3413/684, 6721/1040

1. What is the HCF of 3413,6721?

The HCF of 3413,6721 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 3413/684, 6721/1040?

Answer: GCF of Numerators as per given numbers 3413/684, 6721/1040 is

GCF of Numerators i.e. for 3413,6721 is 1

LCM of denominators i.e. for 684,1040 is 177840.

Thus, GCF of Fractions is 1/177840.Finally, GCF of Fractions for 3413/684, 6721/1040 is 1/177840.