How to Find GCF of 34/76, 29/53, 423/764?

GCF of 34/76, 29/53, 423/764

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 34/76, 29/53, 423/764 i.e 1/769348 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/76, 29/53, 423/764.

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 34/76,29/53,423/764?

Given fractions are 34/76,29/53,423/764

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 34/76,29/53,423/764, numerators are 34,29,423

Denominators are 76,53,764

The GCF of 34,29,423 is 1 .

LCM of 76,53,764 is 769348.

The greatest common factor of 34/76,29/53,423/764 = [GCF of 34,29,423]/[LCM of 76,53,764]= 1/769348

Therefore, the GCF of 34/76,29/53,423/764 is 1/769348.

Greatest Common Factor of 34,29,423

To find the highest common factor of 34,29,423, 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 29 are 1, 29

The factors of 423 are 1, 3, 9, 47, 141, 423

The HCF of 34,29,423 is 1.

Lets's calculate GCF of 34,29,423

Greatest Common Factor (GCF) of 34,29,423 By Common Division

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

Greatest Common Factor of 34,29,423 By Matching Biggest Common Factor Method

Now, list down the factors of 34

1,2,17,34

Now, list down the factors of 29

1,29

Now, list down the factors of 423

1,3,9,47,141,423

Greatest Common Factor

We found the factors 34,29,423 . The biggest common factor number is the GCF number.
So the greatest common factor 34,29,423 is 1.

Lets's calculate LCM of 76,53,764

Lowest Common Multiple of 76,53,764 using Common Division

2	76, 53, 764
2	38, 53, 382
	19, 53, 191

∴ So the LCM of the given numbers is 2 x 2 x 19 x 53 x 191 = 769348

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/769348

Therefore, the GCF of Fractions 34/76,29/53,423/764 is 1/769348

Least Common Multiple of 76,53,764 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 76,53,764 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,53,764) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(76,53,764) x common factors =1 x 4 = 4

LCM(76,53,764) = ( 76 × 53 × 764 ) / 4

LCM(76,53,764) = 3077392 / 4

LCM(76,53,764) = 769348

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 34/76, 29/53, 423/764

1. What is the HCF of 34,29,423?

The HCF of 34,29,423 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 34/76, 29/53, 423/764?

Answer: GCF of Numerators as per given numbers 34/76, 29/53, 423/764 is

GCF of Numerators i.e. for 34,29,423 is 1

LCM of denominators i.e. for 76,53,764 is 769348.

Thus, GCF of Fractions is 1/769348.Finally, GCF of Fractions for 34/76, 29/53, 423/764 is 1/769348.