How to Find GCF of 51/72, 71/33, 578/416?

GCF of 51/72, 71/33, 578/416

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 51/72, 71/33, 578/416 i.e 1/41184 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/72, 71/33, 578/416.

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 51/72,71/33,578/416?

Given fractions are 51/72,71/33,578/416

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 51/72,71/33,578/416, numerators are 51,71,578

Denominators are 72,33,416

The GCF of 51,71,578 is 1 .

LCM of 72,33,416 is 41184.

The greatest common factor of 51/72,71/33,578/416 = [GCF of 51,71,578]/[LCM of 72,33,416]= 1/41184

Therefore, the GCF of 51/72,71/33,578/416 is 1/41184.

Greatest Common Factor of 51,71,578

To find the highest common factor of 51,71,578, we have to find the factors of both numbers and list the highest common factor.

The factors of 51 are 1, 3, 17, 51

The factors of 71 are 1, 71

The factors of 578 are 1, 2, 17, 34, 289, 578

The HCF of 51,71,578 is 1.

Lets's calculate GCF of 51,71,578

Greatest Common Factor (GCF) of 51,71,578 By Common Division

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

Greatest Common Factor of 51,71,578 By Matching Biggest Common Factor Method

Now, list down the factors of 51

1,3,17,51

Now, list down the factors of 71

1,71

Now, list down the factors of 578

1,2,17,34,289,578

Greatest Common Factor

We found the factors 51,71,578 . The biggest common factor number is the GCF number.
So the greatest common factor 51,71,578 is 1.

Lets's calculate LCM of 72,33,416

Lowest Common Multiple of 72,33,416 using Common Division

2	72, 33, 416
2	36, 33, 208
2	18, 33, 104
3	9, 33, 52
	3, 11, 52

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 11 x 52 = 41184

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/41184

Therefore, the GCF of Fractions 51/72,71/33,578/416 is 1/41184

Least Common Multiple of 72,33,416 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 72,33,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(72,33,416) = 1

common factors(in case of two or more numbers have common factors) = 24

GCF(72,33,416) x common factors =1 x 24 = 24

LCM(72,33,416) = ( 72 × 33 × 416 ) / 24

LCM(72,33,416) = 988416 / 24

LCM(72,33,416) = 41184

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 51/72, 71/33, 578/416

1. What is the HCF of 51,71,578?

The HCF of 51,71,578 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 51/72, 71/33, 578/416?

Answer: GCF of Numerators as per given numbers 51/72, 71/33, 578/416 is

GCF of Numerators i.e. for 51,71,578 is 1

LCM of denominators i.e. for 72,33,416 is 41184.

Thus, GCF of Fractions is 1/41184.Finally, GCF of Fractions for 51/72, 71/33, 578/416 is 1/41184.