How to Find GCF of 406/891, 1702/1309?

GCF of 406/891, 1702/1309

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 406/891, 1702/1309 i.e 2/106029 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/891, 1702/1309.

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 406/891,1702/1309?

Given fractions are 406/891,1702/1309

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 406/891,1702/1309, numerators are 406,1702

Denominators are 891,1309

The GCF of 406,1702 is 2 .

LCM of 891,1309 is 106029.

The greatest common factor of 406/891,1702/1309 = [GCF of 406,1702]/[LCM of 891,1309]= 2/106029

Therefore, the GCF of 406/891,1702/1309 is 2/106029.

Greatest Common Factor of 406,1702

To find the highest common factor of 406,1702, we have to find the factors of both numbers and list the highest common factor.

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The factors of 1702 are 1, 2, 23, 37, 46, 74, 851, 1702

The HCF of 406,1702 is 2.

Lets's calculate GCF of 406,1702

Greatest Common Factor (GCF) of 406,1702 By Common Division

2	406, 1702
	203, 851

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 406,1702 By Matching Biggest Common Factor Method

Now, list down the factors of 406

1,2,7,14,29,58,203,406

Now, list down the factors of 1702

1,2,23,37,46,74,851,1702

Greatest Common Factor

We found the factors 406,1702 . The biggest common factor number is the GCF number.
So the greatest common factor 406,1702 is 2.

Lets's calculate LCM of 891,1309

Lowest Common Multiple of 891,1309 using Common Division

11	891, 1309
	81, 119

∴ So the LCM of the given numbers is 11 x 81 x 119 = 106029

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/106029

Therefore, the GCF of Fractions 406/891,1702/1309 is 2/106029

Least Common Multiple of 891,1309 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 891,1309 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(891,1309) = 11

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

GCF(891,1309) x common factors =11 x 1 = 11

LCM(891,1309) = ( 891 × 1309 ) / 11

LCM(891,1309) = 1166319 / 11

LCM(891,1309) = 106029

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FAQs on GCF of Fractions of 406/891, 1702/1309

1. What is the HCF of 406,1702?

The HCF of 406,1702 is 2

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 406/891, 1702/1309?

Answer: GCF of Numerators as per given numbers 406/891, 1702/1309 is

GCF of Numerators i.e. for 406,1702 is 2

LCM of denominators i.e. for 891,1309 is 106029.

Thus, GCF of Fractions is 2/106029.Finally, GCF of Fractions for 406/891, 1702/1309 is 2/106029.