How to Find GCF of 4106/414, 4003/7659?

GCF of 4106/414, 4003/7659

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 4106/414, 4003/7659 i.e 1/15318 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4106/414, 4003/7659.

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 4106/414,4003/7659?

Given fractions are 4106/414,4003/7659

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 4106/414,4003/7659, numerators are 4106,4003

Denominators are 414,7659

The GCF of 4106,4003 is 1 .

LCM of 414,7659 is 15318.

The greatest common factor of 4106/414,4003/7659 = [GCF of 4106,4003]/[LCM of 414,7659]= 1/15318

Therefore, the GCF of 4106/414,4003/7659 is 1/15318.

Greatest Common Factor of 4106,4003

To find the highest common factor of 4106,4003, we have to find the factors of both numbers and list the highest common factor.

The factors of 4106 are 1, 2, 2053, 4106

The factors of 4003 are 1, 4003

The HCF of 4106,4003 is 1.

Lets's calculate GCF of 4106,4003

Greatest Common Factor (GCF) of 4106,4003 By Common Division

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

Greatest Common Factor of 4106,4003 By Matching Biggest Common Factor Method

Now, list down the factors of 4106

1,2,2053,4106

Now, list down the factors of 4003

1,4003

Greatest Common Factor

We found the factors 4106,4003 . The biggest common factor number is the GCF number.
So the greatest common factor 4106,4003 is 1.

Lets's calculate LCM of 414,7659

Lowest Common Multiple of 414,7659 using Common Division

3	414, 7659
3	138, 2553
23	46, 851
	2, 37

∴ So the LCM of the given numbers is 3 x 3 x 23 x 2 x 37 = 15318

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15318

Therefore, the GCF of Fractions 4106/414,4003/7659 is 1/15318

Least Common Multiple of 414,7659 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 414,7659 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(414,7659) = 207

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

GCF(414,7659) x common factors =207 x 1 = 207

LCM(414,7659) = ( 414 × 7659 ) / 207

LCM(414,7659) = 3170826 / 207

LCM(414,7659) = 15318

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FAQs on GCF of Fractions of 4106/414, 4003/7659

1. What is the HCF of 4106,4003?

The HCF of 4106,4003 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 4106/414, 4003/7659?

Answer: GCF of Numerators as per given numbers 4106/414, 4003/7659 is

GCF of Numerators i.e. for 4106,4003 is 1

LCM of denominators i.e. for 414,7659 is 15318.

Thus, GCF of Fractions is 1/15318.Finally, GCF of Fractions for 4106/414, 4003/7659 is 1/15318.