How to Find GCF of 97/78, 33/120, 206/510?

GCF of 97/78, 33/120, 206/510

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 97/78, 33/120, 206/510 i.e 1/26520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 97/78, 33/120, 206/510.

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 97/78,33/120,206/510?

Given fractions are 97/78,33/120,206/510

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 97/78,33/120,206/510, numerators are 97,33,206

Denominators are 78,120,510

The GCF of 97,33,206 is 1 .

LCM of 78,120,510 is 26520.

The greatest common factor of 97/78,33/120,206/510 = [GCF of 97,33,206]/[LCM of 78,120,510]= 1/26520

Therefore, the GCF of 97/78,33/120,206/510 is 1/26520.

Greatest Common Factor of 97,33,206

To find the highest common factor of 97,33,206, we have to find the factors of both numbers and list the highest common factor.

The factors of 97 are 1, 97

The factors of 33 are 1, 3, 11, 33

The factors of 206 are 1, 2, 103, 206

The HCF of 97,33,206 is 1.

Lets's calculate GCF of 97,33,206

Greatest Common Factor (GCF) of 97,33,206 By Common Division

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

Greatest Common Factor of 97,33,206 By Matching Biggest Common Factor Method

Now, list down the factors of 97

1,97

Now, list down the factors of 33

1,3,11,33

Now, list down the factors of 206

1,2,103,206

Greatest Common Factor

We found the factors 97,33,206 . The biggest common factor number is the GCF number.
So the greatest common factor 97,33,206 is 1.

Lets's calculate LCM of 78,120,510

Lowest Common Multiple of 78,120,510 using Common Division

2	78, 120, 510
3	39, 60, 255
5	13, 20, 85
	13, 4, 17

∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 4 x 17 = 26520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26520

Therefore, the GCF of Fractions 97/78,33/120,206/510 is 1/26520

Least Common Multiple of 78,120,510 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 78,120,510 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,120,510) = 6

common factors(in case of two or more numbers have common factors) = 30

GCF(78,120,510) x common factors =6 x 30 = 180

LCM(78,120,510) = ( 78 × 120 × 510 ) / 180

LCM(78,120,510) = 4773600 / 180

LCM(78,120,510) = 26520

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FAQs on GCF of Fractions of 97/78, 33/120, 206/510

1. What is the HCF of 97,33,206?

The HCF of 97,33,206 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 97/78, 33/120, 206/510?

Answer: GCF of Numerators as per given numbers 97/78, 33/120, 206/510 is

GCF of Numerators i.e. for 97,33,206 is 1

LCM of denominators i.e. for 78,120,510 is 26520.

Thus, GCF of Fractions is 1/26520.Finally, GCF of Fractions for 97/78, 33/120, 206/510 is 1/26520.