How to Find GCF of 51/89, 87/45, 74/19?

GCF of 51/89, 87/45, 74/19

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 51/89, 87/45, 74/19 i.e 1/76095 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/89, 87/45, 74/19.

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 51/89,87/45,74/19?

Given fractions are 51/89,87/45,74/19

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 51/89,87/45,74/19, numerators are 51,87,74

Denominators are 89,45,19

The GCF of 51,87,74 is 1 .

LCM of 89,45,19 is 76095.

The greatest common factor of 51/89,87/45,74/19 = [GCF of 51,87,74]/[LCM of 89,45,19]= 1/76095

Therefore, the GCF of 51/89,87/45,74/19 is 1/76095.

Greatest Common Factor of 51,87,74

To find the highest common factor of 51,87,74, 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 87 are 1, 3, 29, 87

The factors of 74 are 1, 2, 37, 74

The HCF of 51,87,74 is 1.

Lets's calculate GCF of 51,87,74

Greatest Common Factor (GCF) of 51,87,74 By Common Division

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

Greatest Common Factor of 51,87,74 By Matching Biggest Common Factor Method

Now, list down the factors of 51

1,3,17,51

Now, list down the factors of 87

1,3,29,87

Now, list down the factors of 74

1,2,37,74

Greatest Common Factor

We found the factors 51,87,74 . The biggest common factor number is the GCF number.
So the greatest common factor 51,87,74 is 1.

Lets's calculate LCM of 89,45,19

Lowest Common Multiple of 89,45,19 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 76095

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/76095

Therefore, the GCF of Fractions 51/89,87/45,74/19 is 1/76095

Least Common Multiple of 89,45,19 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 89,45,19 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(89,45,19) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(89,45,19) x common factors =1 x 1 = 1

LCM(89,45,19) = ( 89 × 45 × 19 ) / 1

LCM(89,45,19) = 76095 / 1

LCM(89,45,19) = 76095

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FAQs on GCF of Fractions of 51/89, 87/45, 74/19

1. What is the HCF of 51,87,74?

The HCF of 51,87,74 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 51/89, 87/45, 74/19?

Answer: GCF of Numerators as per given numbers 51/89, 87/45, 74/19 is

GCF of Numerators i.e. for 51,87,74 is 1

LCM of denominators i.e. for 89,45,19 is 76095.

Thus, GCF of Fractions is 1/76095.Finally, GCF of Fractions for 51/89, 87/45, 74/19 is 1/76095.