How to Find GCF of 920/988, 1109/772?

GCF of 920/988, 1109/772

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 920/988, 1109/772 i.e 1/190684 easily. The following is the detailed procedure to determine the greatest common factor of fractions 920/988, 1109/772.

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 920/988,1109/772?

Given fractions are 920/988,1109/772

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 920/988,1109/772, numerators are 920,1109

Denominators are 988,772

The GCF of 920,1109 is 1 .

LCM of 988,772 is 190684.

The greatest common factor of 920/988,1109/772 = [GCF of 920,1109]/[LCM of 988,772]= 1/190684

Therefore, the GCF of 920/988,1109/772 is 1/190684.

Greatest Common Factor of 920,1109

To find the highest common factor of 920,1109, we have to find the factors of both numbers and list the highest common factor.

The factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920

The factors of 1109 are 1, 1109

The HCF of 920,1109 is 1.

Lets's calculate GCF of 920,1109

Greatest Common Factor (GCF) of 920,1109 By Common Division

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

Greatest Common Factor of 920,1109 By Matching Biggest Common Factor Method

Now, list down the factors of 920

1,2,4,5,8,10,20,23,40,46,92,115,184,230,460,920

Now, list down the factors of 1109

1,1109

Greatest Common Factor

We found the factors 920,1109 . The biggest common factor number is the GCF number.
So the greatest common factor 920,1109 is 1.

Lets's calculate LCM of 988,772

Lowest Common Multiple of 988,772 using Common Division

2	988, 772
2	494, 386
	247, 193

∴ So the LCM of the given numbers is 2 x 2 x 247 x 193 = 190684

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/190684

Therefore, the GCF of Fractions 920/988,1109/772 is 1/190684

Least Common Multiple of 988,772 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 988,772 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(988,772) = 4

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

GCF(988,772) x common factors =4 x 1 = 4

LCM(988,772) = ( 988 × 772 ) / 4

LCM(988,772) = 762736 / 4

LCM(988,772) = 190684

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FAQs on GCF of Fractions of 920/988, 1109/772

1. What is the HCF of 920,1109?

The HCF of 920,1109 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 920/988, 1109/772?

Answer: GCF of Numerators as per given numbers 920/988, 1109/772 is

GCF of Numerators i.e. for 920,1109 is 1

LCM of denominators i.e. for 988,772 is 190684.

Thus, GCF of Fractions is 1/190684.Finally, GCF of Fractions for 920/988, 1109/772 is 1/190684.