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GCF of 989/34, 109/1946

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 989/34, 109/1946 i.e 1/33082 easily. The following is the detailed procedure to determine the greatest common factor of fractions 989/34, 109/1946.

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 989/34,109/1946?

Given fractions are 989/34,109/1946

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 989/34,109/1946, numerators are 989,109

Denominators are 34,1946

The GCF of 989,109 is 1 .

LCM of 34,1946 is 33082.

The greatest common factor of 989/34,109/1946 = [GCF of 989,109]/[LCM of 34,1946]= 1/33082

Therefore, the GCF of 989/34,109/1946 is 1/33082.

Greatest Common Factor of 989,109

To find the highest common factor of 989,109, we have to find the factors of both numbers and list the highest common factor.

The factors of 989 are 1, 23, 43, 989

The factors of 109 are 1, 109

The HCF of 989,109 is 1.

Lets's calculate GCF of 989,109

Greatest Common Factor (GCF) of 989,109 By Common Division

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

Greatest Common Factor of 989,109 By Matching Biggest Common Factor Method

Greatest Common Factor of 989,109 By Matching Biggest Common Factor Method

Now, list down the factors of 989

:

1,23,43,989

Now, list down the factors of 109

:

1,109

Greatest Common Factor

We found the factors 989,109 . The biggest common factor number is the GCF number.
So the greatest common factor 989,109 is 1.

Lets's calculate LCM of 34,1946

Lowest Common Multiple of 34,1946 using Common Division

2 34, 1946
17, 973

∴ So the LCM of the given numbers is 2 x 17 x 973 = 33082

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/33082

Therefore, the GCF of Fractions 989/34,109/1946 is 1/33082

Least Common Multiple of 34,1946 with GCF Formula

Least Common Multiple of 34,1946 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 34,1946 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,1946) = 2

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

GCF(34,1946) x common factors =2 x 1 = 2

LCM(34,1946) = ( 34 × 1946 ) / 2

LCM(34,1946) = 66164 / 2

LCM(34,1946) = 33082


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FAQs on GCF of Fractions of 989/34, 109/1946

1. What is the HCF of 989,109?

The HCF of 989,109 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 989/34, 109/1946?

Answer: GCF of Numerators as per given numbers 989/34, 109/1946 is

GCF of Numerators i.e. for 989,109 is 1

LCM of denominators i.e. for 34,1946 is 33082.

Thus, GCF of Fractions is 1/33082.Finally, GCF of Fractions for 989/34, 109/1946 is 1/33082.