How to Find GCF of 66/278, 65/775, 349/104?

GCF of 66/278, 65/775, 349/104

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 66/278, 65/775, 349/104 i.e 1/11203400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/278, 65/775, 349/104.

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 66/278,65/775,349/104?

Given fractions are 66/278,65/775,349/104

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 66/278,65/775,349/104, numerators are 66,65,349

Denominators are 278,775,104

The GCF of 66,65,349 is 1 .

LCM of 278,775,104 is 11203400.

The greatest common factor of 66/278,65/775,349/104 = [GCF of 66,65,349]/[LCM of 278,775,104]= 1/11203400

Therefore, the GCF of 66/278,65/775,349/104 is 1/11203400.

Greatest Common Factor of 66,65,349

To find the highest common factor of 66,65,349, we have to find the factors of both numbers and list the highest common factor.

The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66

The factors of 65 are 1, 5, 13, 65

The factors of 349 are 1, 349

The HCF of 66,65,349 is 1.

Lets's calculate GCF of 66,65,349

Greatest Common Factor (GCF) of 66,65,349 By Common Division

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

Greatest Common Factor of 66,65,349 By Matching Biggest Common Factor Method

Now, list down the factors of 66

1,2,3,6,11,22,33,66

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 349

1,349

Greatest Common Factor

We found the factors 66,65,349 . The biggest common factor number is the GCF number.
So the greatest common factor 66,65,349 is 1.

Lets's calculate LCM of 278,775,104

Lowest Common Multiple of 278,775,104 using Common Division

2	278, 775, 104
	139, 775, 52

∴ So the LCM of the given numbers is 2 x 139 x 775 x 52 = 11203400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11203400

Therefore, the GCF of Fractions 66/278,65/775,349/104 is 1/11203400

Least Common Multiple of 278,775,104 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 278,775,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(278,775,104) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(278,775,104) x common factors =1 x 2 = 2

LCM(278,775,104) = ( 278 × 775 × 104 ) / 2

LCM(278,775,104) = 22406800 / 2

LCM(278,775,104) = 11203400

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FAQs on GCF of Fractions of 66/278, 65/775, 349/104

1. What is the HCF of 66,65,349?

The HCF of 66,65,349 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 66/278, 65/775, 349/104?

Answer: GCF of Numerators as per given numbers 66/278, 65/775, 349/104 is

GCF of Numerators i.e. for 66,65,349 is 1

LCM of denominators i.e. for 278,775,104 is 11203400.

Thus, GCF of Fractions is 1/11203400.Finally, GCF of Fractions for 66/278, 65/775, 349/104 is 1/11203400.