How to Find GCF of 160/998, 1929/1226?

GCF of 160/998, 1929/1226

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 160/998, 1929/1226 i.e 1/611774 easily. The following is the detailed procedure to determine the greatest common factor of fractions 160/998, 1929/1226.

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 160/998,1929/1226?

Given fractions are 160/998,1929/1226

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 160/998,1929/1226, numerators are 160,1929

Denominators are 998,1226

The GCF of 160,1929 is 1 .

LCM of 998,1226 is 611774.

The greatest common factor of 160/998,1929/1226 = [GCF of 160,1929]/[LCM of 998,1226]= 1/611774

Therefore, the GCF of 160/998,1929/1226 is 1/611774.

Greatest Common Factor of 160,1929

To find the highest common factor of 160,1929, we have to find the factors of both numbers and list the highest common factor.

The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160

The factors of 1929 are 1, 3, 643, 1929

The HCF of 160,1929 is 1.

Lets's calculate GCF of 160,1929

Greatest Common Factor (GCF) of 160,1929 By Common Division

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

Greatest Common Factor of 160,1929 By Matching Biggest Common Factor Method

Now, list down the factors of 160

1,2,4,5,8,10,16,20,32,40,80,160

Now, list down the factors of 1929

1,3,643,1929

Greatest Common Factor

We found the factors 160,1929 . The biggest common factor number is the GCF number.
So the greatest common factor 160,1929 is 1.

Lets's calculate LCM of 998,1226

Lowest Common Multiple of 998,1226 using Common Division

2	998, 1226
	499, 613

∴ So the LCM of the given numbers is 2 x 499 x 613 = 611774

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/611774

Therefore, the GCF of Fractions 160/998,1929/1226 is 1/611774

Least Common Multiple of 998,1226 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 998,1226 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(998,1226) = 2

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

GCF(998,1226) x common factors =2 x 1 = 2

LCM(998,1226) = ( 998 × 1226 ) / 2

LCM(998,1226) = 1223548 / 2

LCM(998,1226) = 611774

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FAQs on GCF of Fractions of 160/998, 1929/1226

1. What is the HCF of 160,1929?

The HCF of 160,1929 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 160/998, 1929/1226?

Answer: GCF of Numerators as per given numbers 160/998, 1929/1226 is

GCF of Numerators i.e. for 160,1929 is 1

LCM of denominators i.e. for 998,1226 is 611774.

Thus, GCF of Fractions is 1/611774.Finally, GCF of Fractions for 160/998, 1929/1226 is 1/611774.