How to Find GCF of 51/80, 37/22, 596/728?

GCF of 51/80, 37/22, 596/728

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 51/80, 37/22, 596/728 i.e 1/80080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/80, 37/22, 596/728.

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 51/80,37/22,596/728?

Given fractions are 51/80,37/22,596/728

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 51/80,37/22,596/728, numerators are 51,37,596

Denominators are 80,22,728

The GCF of 51,37,596 is 1 .

LCM of 80,22,728 is 80080.

The greatest common factor of 51/80,37/22,596/728 = [GCF of 51,37,596]/[LCM of 80,22,728]= 1/80080

Therefore, the GCF of 51/80,37/22,596/728 is 1/80080.

Greatest Common Factor of 51,37,596

To find the highest common factor of 51,37,596, 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 37 are 1, 37

The factors of 596 are 1, 2, 4, 149, 298, 596

The HCF of 51,37,596 is 1.

Lets's calculate GCF of 51,37,596

Greatest Common Factor (GCF) of 51,37,596 By Common Division

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

Greatest Common Factor of 51,37,596 By Matching Biggest Common Factor Method

Now, list down the factors of 51

1,3,17,51

Now, list down the factors of 37

1,37

Now, list down the factors of 596

1,2,4,149,298,596

Greatest Common Factor

We found the factors 51,37,596 . The biggest common factor number is the GCF number.
So the greatest common factor 51,37,596 is 1.

Lets's calculate LCM of 80,22,728

Lowest Common Multiple of 80,22,728 using Common Division

2	80, 22, 728
2	40, 11, 364
2	20, 11, 182
	10, 11, 91

∴ So the LCM of the given numbers is 2 x 2 x 2 x 10 x 11 x 91 = 80080

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/80080

Therefore, the GCF of Fractions 51/80,37/22,596/728 is 1/80080

Least Common Multiple of 80,22,728 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 80,22,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(80,22,728) = 2

common factors(in case of two or more numbers have common factors) = 8

GCF(80,22,728) x common factors =2 x 8 = 16

LCM(80,22,728) = ( 80 × 22 × 728 ) / 16

LCM(80,22,728) = 1281280 / 16

LCM(80,22,728) = 80080

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FAQs on GCF of Fractions of 51/80, 37/22, 596/728

1. What is the HCF of 51,37,596?

The HCF of 51,37,596 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 51/80, 37/22, 596/728?

Answer: GCF of Numerators as per given numbers 51/80, 37/22, 596/728 is

GCF of Numerators i.e. for 51,37,596 is 1

LCM of denominators i.e. for 80,22,728 is 80080.

Thus, GCF of Fractions is 1/80080.Finally, GCF of Fractions for 51/80, 37/22, 596/728 is 1/80080.