How to Find GCF of 34/66, 57/13, 272/65?

GCF of 34/66, 57/13, 272/65

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 34/66, 57/13, 272/65 i.e 1/4290 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/66, 57/13, 272/65.

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 34/66,57/13,272/65?

Given fractions are 34/66,57/13,272/65

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 34/66,57/13,272/65, numerators are 34,57,272

Denominators are 66,13,65

The GCF of 34,57,272 is 1 .

LCM of 66,13,65 is 4290.

The greatest common factor of 34/66,57/13,272/65 = [GCF of 34,57,272]/[LCM of 66,13,65]= 1/4290

Therefore, the GCF of 34/66,57/13,272/65 is 1/4290.

Greatest Common Factor of 34,57,272

To find the highest common factor of 34,57,272, we have to find the factors of both numbers and list the highest common factor.

The factors of 34 are 1, 2, 17, 34

The factors of 57 are 1, 3, 19, 57

The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272

The HCF of 34,57,272 is 1.

Lets's calculate GCF of 34,57,272

Greatest Common Factor (GCF) of 34,57,272 By Common Division

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

Greatest Common Factor of 34,57,272 By Matching Biggest Common Factor Method

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 57

1,3,19,57

Now, list down the factors of 272

1,2,4,8,16,17,34,68,136,272

Greatest Common Factor

We found the factors 34,57,272 . The biggest common factor number is the GCF number.
So the greatest common factor 34,57,272 is 1.

Lets's calculate LCM of 66,13,65

Lowest Common Multiple of 66,13,65 using Common Division

13	66, 13, 65
	66, 1, 5

∴ So the LCM of the given numbers is 13 x 66 x 1 x 5 = 4290

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4290

Therefore, the GCF of Fractions 34/66,57/13,272/65 is 1/4290

Least Common Multiple of 66,13,65 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 66,13,65 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(66,13,65) = 1

common factors(in case of two or more numbers have common factors) = 13

GCF(66,13,65) x common factors =1 x 13 = 13

LCM(66,13,65) = ( 66 × 13 × 65 ) / 13

LCM(66,13,65) = 55770 / 13

LCM(66,13,65) = 4290

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FAQs on GCF of Fractions of 34/66, 57/13, 272/65

1. What is the HCF of 34,57,272?

The HCF of 34,57,272 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 34/66, 57/13, 272/65?

Answer: GCF of Numerators as per given numbers 34/66, 57/13, 272/65 is

GCF of Numerators i.e. for 34,57,272 is 1

LCM of denominators i.e. for 66,13,65 is 4290.

Thus, GCF of Fractions is 1/4290.Finally, GCF of Fractions for 34/66, 57/13, 272/65 is 1/4290.