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GCF of 414/998, 919/706

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 414/998, 919/706 i.e 1/352294 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/998, 919/706.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 414/998,919/706?

Given fractions are 414/998,919/706

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 414/998,919/706, numerators are 414,919

Denominators are 998,706

The GCF of 414,919 is 1 .

LCM of 998,706 is 352294.

The greatest common factor of 414/998,919/706 = [GCF of 414,919]/[LCM of 998,706]= 1/352294

Therefore, the GCF of 414/998,919/706 is 1/352294.

Greatest Common Factor of 414,919

To find the highest common factor of 414,919, we have to find the factors of both numbers and list the highest common factor.

The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

The factors of 919 are 1, 919

The HCF of 414,919 is 1.

Lets's calculate GCF of 414,919

Greatest Common Factor (GCF) of 414,919 By Common Division

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

Greatest Common Factor of 414,919 By Matching Biggest Common Factor Method

Greatest Common Factor of 414,919 By Matching Biggest Common Factor Method

Now, list down the factors of 414

:

1,2,3,6,9,18,23,46,69,138,207,414

Now, list down the factors of 919

:

1,919

Greatest Common Factor

We found the factors 414,919 . The biggest common factor number is the GCF number.
So the greatest common factor 414,919 is 1.

Lets's calculate LCM of 998,706

Lowest Common Multiple of 998,706 using Common Division

2 998, 706
499, 353

∴ So the LCM of the given numbers is 2 x 499 x 353 = 352294

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/352294

Therefore, the GCF of Fractions 414/998,919/706 is 1/352294

Least Common Multiple of 998,706 with GCF Formula

Least Common Multiple of 998,706 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 998,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(998,706) = 2

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

GCF(998,706) x common factors =2 x 1 = 2

LCM(998,706) = ( 998 × 706 ) / 2

LCM(998,706) = 704588 / 2

LCM(998,706) = 352294


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FAQs on GCF of Fractions of 414/998, 919/706

1. What is the HCF of 414,919?

The HCF of 414,919 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 414/998, 919/706?

Answer: GCF of Numerators as per given numbers 414/998, 919/706 is

GCF of Numerators i.e. for 414,919 is 1

LCM of denominators i.e. for 998,706 is 352294.

Thus, GCF of Fractions is 1/352294.Finally, GCF of Fractions for 414/998, 919/706 is 1/352294.