How to Find GCF of 69/30, 10/41, 254/768?

GCF of 69/30, 10/41, 254/768

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 69/30, 10/41, 254/768 i.e 1/157440 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/30, 10/41, 254/768.

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 69/30,10/41,254/768?

Given fractions are 69/30,10/41,254/768

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 69/30,10/41,254/768, numerators are 69,10,254

Denominators are 30,41,768

The GCF of 69,10,254 is 1 .

LCM of 30,41,768 is 157440.

The greatest common factor of 69/30,10/41,254/768 = [GCF of 69,10,254]/[LCM of 30,41,768]= 1/157440

Therefore, the GCF of 69/30,10/41,254/768 is 1/157440.

Greatest Common Factor of 69,10,254

To find the highest common factor of 69,10,254, we have to find the factors of both numbers and list the highest common factor.

The factors of 69 are 1, 3, 23, 69

The factors of 10 are 1, 2, 5, 10

The factors of 254 are 1, 2, 127, 254

The HCF of 69,10,254 is 1.

Lets's calculate GCF of 69,10,254

Greatest Common Factor (GCF) of 69,10,254 By Common Division

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

Greatest Common Factor of 69,10,254 By Matching Biggest Common Factor Method

Now, list down the factors of 69

1,3,23,69

Now, list down the factors of 10

1,2,5,10

Now, list down the factors of 254

1,2,127,254

Greatest Common Factor

We found the factors 69,10,254 . The biggest common factor number is the GCF number.
So the greatest common factor 69,10,254 is 1.

Lets's calculate LCM of 30,41,768

Lowest Common Multiple of 30,41,768 using Common Division

2	30, 41, 768
3	15, 41, 384
	5, 41, 128

∴ So the LCM of the given numbers is 2 x 3 x 5 x 41 x 128 = 157440

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/157440

Therefore, the GCF of Fractions 69/30,10/41,254/768 is 1/157440

Least Common Multiple of 30,41,768 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 30,41,768 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,41,768) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(30,41,768) x common factors =1 x 6 = 6

LCM(30,41,768) = ( 30 × 41 × 768 ) / 6

LCM(30,41,768) = 944640 / 6

LCM(30,41,768) = 157440

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FAQs on GCF of Fractions of 69/30, 10/41, 254/768

1. What is the HCF of 69,10,254?

The HCF of 69,10,254 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 69/30, 10/41, 254/768?

Answer: GCF of Numerators as per given numbers 69/30, 10/41, 254/768 is

GCF of Numerators i.e. for 69,10,254 is 1

LCM of denominators i.e. for 30,41,768 is 157440.

Thus, GCF of Fractions is 1/157440.Finally, GCF of Fractions for 69/30, 10/41, 254/768 is 1/157440.