How to Find GCF of 174/30, 214/89, 507/29?

GCF of 174/30, 214/89, 507/29

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 174/30, 214/89, 507/29 i.e 1/77430 easily. The following is the detailed procedure to determine the greatest common factor of fractions 174/30, 214/89, 507/29.

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 174/30,214/89,507/29?

Given fractions are 174/30,214/89,507/29

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 174/30,214/89,507/29, numerators are 174,214,507

Denominators are 30,89,29

The GCF of 174,214,507 is 1 .

LCM of 30,89,29 is 77430.

The greatest common factor of 174/30,214/89,507/29 = [GCF of 174,214,507]/[LCM of 30,89,29]= 1/77430

Therefore, the GCF of 174/30,214/89,507/29 is 1/77430.

Greatest Common Factor of 174,214,507

To find the highest common factor of 174,214,507, we have to find the factors of both numbers and list the highest common factor.

The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174

The factors of 214 are 1, 2, 107, 214

The factors of 507 are 1, 3, 13, 39, 169, 507

The HCF of 174,214,507 is 1.

Lets's calculate GCF of 174,214,507

Greatest Common Factor (GCF) of 174,214,507 By Common Division

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

Greatest Common Factor of 174,214,507 By Matching Biggest Common Factor Method

Now, list down the factors of 174

1,2,3,6,29,58,87,174

Now, list down the factors of 214

1,2,107,214

Now, list down the factors of 507

1,3,13,39,169,507

Greatest Common Factor

We found the factors 174,214,507 . The biggest common factor number is the GCF number.
So the greatest common factor 174,214,507 is 1.

Lets's calculate LCM of 30,89,29

Lowest Common Multiple of 30,89,29 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 77430

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/77430

Therefore, the GCF of Fractions 174/30,214/89,507/29 is 1/77430

Least Common Multiple of 30,89,29 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 30,89,29 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,89,29) = 1

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

GCF(30,89,29) x common factors =1 x 1 = 1

LCM(30,89,29) = ( 30 × 89 × 29 ) / 1

LCM(30,89,29) = 77430 / 1

LCM(30,89,29) = 77430

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FAQs on GCF of Fractions of 174/30, 214/89, 507/29

1. What is the HCF of 174,214,507?

The HCF of 174,214,507 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 174/30, 214/89, 507/29?

Answer: GCF of Numerators as per given numbers 174/30, 214/89, 507/29 is

GCF of Numerators i.e. for 174,214,507 is 1

LCM of denominators i.e. for 30,89,29 is 77430.

Thus, GCF of Fractions is 1/77430.Finally, GCF of Fractions for 174/30, 214/89, 507/29 is 1/77430.