How to Find GCF of 6986/406, 3164/2385?

GCF of 6986/406, 3164/2385

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 6986/406, 3164/2385 i.e 14/968310 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6986/406, 3164/2385.

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 6986/406,3164/2385?

Given fractions are 6986/406,3164/2385

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 6986/406,3164/2385, numerators are 6986,3164

Denominators are 406,2385

The GCF of 6986,3164 is 14 .

LCM of 406,2385 is 968310.

The greatest common factor of 6986/406,3164/2385 = [GCF of 6986,3164]/[LCM of 406,2385]= 14/968310

Therefore, the GCF of 6986/406,3164/2385 is 14/968310.

Greatest Common Factor of 6986,3164

To find the highest common factor of 6986,3164, we have to find the factors of both numbers and list the highest common factor.

The factors of 6986 are 1, 2, 7, 14, 499, 998, 3493, 6986

The factors of 3164 are 1, 2, 4, 7, 14, 28, 113, 226, 452, 791, 1582, 3164

The HCF of 6986,3164 is 14.

Lets's calculate GCF of 6986,3164

Greatest Common Factor (GCF) of 6986,3164 By Common Division

2	6986, 3164
7	3493, 1582
	499, 226

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 6986,3164 By Matching Biggest Common Factor Method

Now, list down the factors of 6986

1,2,7,14,499,998,3493,6986

Now, list down the factors of 3164

1,2,4,7,14,28,113,226,452,791,1582,3164

Greatest Common Factor

We found the factors 6986,3164 . The biggest common factor number is the GCF number.
So the greatest common factor 6986,3164 is 14.

Lets's calculate LCM of 406,2385

Lowest Common Multiple of 406,2385 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 968310

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/968310

Therefore, the GCF of Fractions 6986/406,3164/2385 is 14/968310

Least Common Multiple of 406,2385 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 406,2385 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(406,2385) = 1

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

GCF(406,2385) x common factors =1 x 1 = 1

LCM(406,2385) = ( 406 × 2385 ) / 1

LCM(406,2385) = 968310 / 1

LCM(406,2385) = 968310

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FAQs on GCF of Fractions of 6986/406, 3164/2385

1. What is the HCF of 6986,3164?

The HCF of 6986,3164 is 14

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 6986/406, 3164/2385?

Answer: GCF of Numerators as per given numbers 6986/406, 3164/2385 is

GCF of Numerators i.e. for 6986,3164 is 14

LCM of denominators i.e. for 406,2385 is 968310.

Thus, GCF of Fractions is 14/968310.Finally, GCF of Fractions for 6986/406, 3164/2385 is 14/968310.