How to Find GCF of 71/429, 27/416, 923/564?

GCF of 71/429, 27/416, 923/564

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 71/429, 27/416, 923/564 i.e 1/645216 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/429, 27/416, 923/564.

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 71/429,27/416,923/564?

Given fractions are 71/429,27/416,923/564

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 71/429,27/416,923/564, numerators are 71,27,923

Denominators are 429,416,564

The GCF of 71,27,923 is 1 .

LCM of 429,416,564 is 645216.

The greatest common factor of 71/429,27/416,923/564 = [GCF of 71,27,923]/[LCM of 429,416,564]= 1/645216

Therefore, the GCF of 71/429,27/416,923/564 is 1/645216.

Greatest Common Factor of 71,27,923

To find the highest common factor of 71,27,923, we have to find the factors of both numbers and list the highest common factor.

The factors of 71 are 1, 71

The factors of 27 are 1, 3, 9, 27

The factors of 923 are 1, 13, 71, 923

The HCF of 71,27,923 is 1.

Lets's calculate GCF of 71,27,923

Greatest Common Factor (GCF) of 71,27,923 By Common Division

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

Greatest Common Factor of 71,27,923 By Matching Biggest Common Factor Method

Now, list down the factors of 71

1,71

Now, list down the factors of 27

1,3,9,27

Now, list down the factors of 923

1,13,71,923

Greatest Common Factor

We found the factors 71,27,923 . The biggest common factor number is the GCF number.
So the greatest common factor 71,27,923 is 1.

Lets's calculate LCM of 429,416,564

Lowest Common Multiple of 429,416,564 using Common Division

2	429, 416, 564
2	429, 208, 282
3	429, 104, 141
13	143, 104, 47
	11, 8, 47

∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 11 x 8 x 47 = 645216

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/645216

Therefore, the GCF of Fractions 71/429,27/416,923/564 is 1/645216

Least Common Multiple of 429,416,564 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 429,416,564 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(429,416,564) = 1

common factors(in case of two or more numbers have common factors) = 156

GCF(429,416,564) x common factors =1 x 156 = 156

LCM(429,416,564) = ( 429 × 416 × 564 ) / 156

LCM(429,416,564) = 100653696 / 156

LCM(429,416,564) = 645216

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 71/429, 27/416, 923/564

1. What is the HCF of 71,27,923?

The HCF of 71,27,923 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 71/429, 27/416, 923/564?

Answer: GCF of Numerators as per given numbers 71/429, 27/416, 923/564 is

GCF of Numerators i.e. for 71,27,923 is 1

LCM of denominators i.e. for 429,416,564 is 645216.

Thus, GCF of Fractions is 1/645216.Finally, GCF of Fractions for 71/429, 27/416, 923/564 is 1/645216.