How to Find GCF of 789/748, 196/986?

GCF of 789/748, 196/986

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 789/748, 196/986 i.e 1/21692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 789/748, 196/986.

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 789/748,196/986?

Given fractions are 789/748,196/986

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 789/748,196/986, numerators are 789,196

Denominators are 748,986

The GCF of 789,196 is 1 .

LCM of 748,986 is 21692.

The greatest common factor of 789/748,196/986 = [GCF of 789,196]/[LCM of 748,986]= 1/21692

Therefore, the GCF of 789/748,196/986 is 1/21692.

Greatest Common Factor of 789,196

To find the highest common factor of 789,196, we have to find the factors of both numbers and list the highest common factor.

The factors of 789 are 1, 3, 263, 789

The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196

The HCF of 789,196 is 1.

Lets's calculate GCF of 789,196

Greatest Common Factor (GCF) of 789,196 By Common Division

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

Greatest Common Factor of 789,196 By Matching Biggest Common Factor Method

Now, list down the factors of 789

1,3,263,789

Now, list down the factors of 196

1,2,4,7,14,28,49,98,196

Greatest Common Factor

We found the factors 789,196 . The biggest common factor number is the GCF number.
So the greatest common factor 789,196 is 1.

Lets's calculate LCM of 748,986

Lowest Common Multiple of 748,986 using Common Division

2	748, 986
17	374, 493
	22, 29

∴ So the LCM of the given numbers is 2 x 17 x 22 x 29 = 21692

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21692

Therefore, the GCF of Fractions 789/748,196/986 is 1/21692

Least Common Multiple of 748,986 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 748,986 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(748,986) = 34

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

GCF(748,986) x common factors =34 x 1 = 34

LCM(748,986) = ( 748 × 986 ) / 34

LCM(748,986) = 737528 / 34

LCM(748,986) = 21692

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FAQs on GCF of Fractions of 789/748, 196/986

1. What is the HCF of 789,196?

The HCF of 789,196 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 789/748, 196/986?

Answer: GCF of Numerators as per given numbers 789/748, 196/986 is

GCF of Numerators i.e. for 789,196 is 1

LCM of denominators i.e. for 748,986 is 21692.

Thus, GCF of Fractions is 1/21692.Finally, GCF of Fractions for 789/748, 196/986 is 1/21692.