How to Find GCF of 406/457, 7729/278?

GCF of 406/457, 7729/278

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 406/457, 7729/278 i.e 1/127046 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/457, 7729/278.

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 406/457,7729/278?

Given fractions are 406/457,7729/278

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 406/457,7729/278, numerators are 406,7729

Denominators are 457,278

The GCF of 406,7729 is 1 .

LCM of 457,278 is 127046.

The greatest common factor of 406/457,7729/278 = [GCF of 406,7729]/[LCM of 457,278]= 1/127046

Therefore, the GCF of 406/457,7729/278 is 1/127046.

Greatest Common Factor of 406,7729

To find the highest common factor of 406,7729, 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 7729 are 1, 59, 131, 7729

The HCF of 406,7729 is 1.

Lets's calculate GCF of 406,7729

Greatest Common Factor (GCF) of 406,7729 By Common Division

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

Greatest Common Factor of 406,7729 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 7729

1,59,131,7729

Greatest Common Factor

We found the factors 406,7729 . The biggest common factor number is the GCF number.
So the greatest common factor 406,7729 is 1.

Lets's calculate LCM of 457,278

Lowest Common Multiple of 457,278 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 127046

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/127046

Therefore, the GCF of Fractions 406/457,7729/278 is 1/127046

Least Common Multiple of 457,278 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 457,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(457,278) = 1

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

GCF(457,278) x common factors =1 x 1 = 1

LCM(457,278) = ( 457 × 278 ) / 1

LCM(457,278) = 127046 / 1

LCM(457,278) = 127046

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FAQs on GCF of Fractions of 406/457, 7729/278

1. What is the HCF of 406,7729?

The HCF of 406,7729 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 406/457, 7729/278?

Answer: GCF of Numerators as per given numbers 406/457, 7729/278 is

GCF of Numerators i.e. for 406,7729 is 1

LCM of denominators i.e. for 457,278 is 127046.

Thus, GCF of Fractions is 1/127046.Finally, GCF of Fractions for 406/457, 7729/278 is 1/127046.