How to Find GCF of 406/149, 5306/7208?

GCF of 406/149, 5306/7208

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 406/149, 5306/7208 i.e 14/1073992 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/149, 5306/7208.

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 406/149,5306/7208?

Given fractions are 406/149,5306/7208

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 406/149,5306/7208, numerators are 406,5306

Denominators are 149,7208

The GCF of 406,5306 is 14 .

LCM of 149,7208 is 1073992.

The greatest common factor of 406/149,5306/7208 = [GCF of 406,5306]/[LCM of 149,7208]= 14/1073992

Therefore, the GCF of 406/149,5306/7208 is 14/1073992.

Greatest Common Factor of 406,5306

To find the highest common factor of 406,5306, 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 5306 are 1, 2, 7, 14, 379, 758, 2653, 5306

The HCF of 406,5306 is 14.

Lets's calculate GCF of 406,5306

Greatest Common Factor (GCF) of 406,5306 By Common Division

2	406, 5306
7	203, 2653
	29, 379

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

Greatest Common Factor of 406,5306 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 5306

1,2,7,14,379,758,2653,5306

Greatest Common Factor

We found the factors 406,5306 . The biggest common factor number is the GCF number.
So the greatest common factor 406,5306 is 14.

Lets's calculate LCM of 149,7208

Lowest Common Multiple of 149,7208 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1073992

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/1073992

Therefore, the GCF of Fractions 406/149,5306/7208 is 14/1073992

Least Common Multiple of 149,7208 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 149,7208 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(149,7208) = 1

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

GCF(149,7208) x common factors =1 x 1 = 1

LCM(149,7208) = ( 149 × 7208 ) / 1

LCM(149,7208) = 1073992 / 1

LCM(149,7208) = 1073992

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FAQs on GCF of Fractions of 406/149, 5306/7208

1. What is the HCF of 406,5306?

The HCF of 406,5306 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 406/149, 5306/7208?

Answer: GCF of Numerators as per given numbers 406/149, 5306/7208 is

GCF of Numerators i.e. for 406,5306 is 14

LCM of denominators i.e. for 149,7208 is 1073992.

Thus, GCF of Fractions is 14/1073992.Finally, GCF of Fractions for 406/149, 5306/7208 is 14/1073992.