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GCF of 970/20, 789/678

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 970/20, 789/678 i.e 1/6780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 970/20, 789/678.

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 970/20,789/678?

Given fractions are 970/20,789/678

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 970/20,789/678, numerators are 970,789

Denominators are 20,678

The GCF of 970,789 is 1 .

LCM of 20,678 is 6780.

The greatest common factor of 970/20,789/678 = [GCF of 970,789]/[LCM of 20,678]= 1/6780

Therefore, the GCF of 970/20,789/678 is 1/6780.

Greatest Common Factor of 970,789

To find the highest common factor of 970,789, we have to find the factors of both numbers and list the highest common factor.

The factors of 970 are 1, 2, 5, 10, 97, 194, 485, 970

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

The HCF of 970,789 is 1.

Lets's calculate GCF of 970,789

Greatest Common Factor (GCF) of 970,789 By Common Division

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

Greatest Common Factor of 970,789 By Matching Biggest Common Factor Method

Greatest Common Factor of 970,789 By Matching Biggest Common Factor Method

Now, list down the factors of 970

:

1,2,5,10,97,194,485,970

Now, list down the factors of 789

:

1,3,263,789

Greatest Common Factor

We found the factors 970,789 . The biggest common factor number is the GCF number.
So the greatest common factor 970,789 is 1.

Lets's calculate LCM of 20,678

Lowest Common Multiple of 20,678 using Common Division

2 20, 678
10, 339

∴ So the LCM of the given numbers is 2 x 10 x 339 = 6780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6780

Therefore, the GCF of Fractions 970/20,789/678 is 1/6780

Least Common Multiple of 20,678 with GCF Formula

Least Common Multiple of 20,678 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 20,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,678) = 2

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

GCF(20,678) x common factors =2 x 1 = 2

LCM(20,678) = ( 20 × 678 ) / 2

LCM(20,678) = 13560 / 2

LCM(20,678) = 6780


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FAQs on GCF of Fractions of 970/20, 789/678

1. What is the HCF of 970,789?

The HCF of 970,789 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 970/20, 789/678?

Answer: GCF of Numerators as per given numbers 970/20, 789/678 is

GCF of Numerators i.e. for 970,789 is 1

LCM of denominators i.e. for 20,678 is 6780.

Thus, GCF of Fractions is 1/6780.Finally, GCF of Fractions for 970/20, 789/678 is 1/6780.