How to Find GCF of 213/746, 650/729?

GCF of 213/746, 650/729

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 213/746, 650/729 i.e 1/543834 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/746, 650/729.

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 213/746,650/729?

Given fractions are 213/746,650/729

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 213/746,650/729, numerators are 213,650

Denominators are 746,729

The GCF of 213,650 is 1 .

LCM of 746,729 is 543834.

The greatest common factor of 213/746,650/729 = [GCF of 213,650]/[LCM of 746,729]= 1/543834

Therefore, the GCF of 213/746,650/729 is 1/543834.

Greatest Common Factor of 213,650

To find the highest common factor of 213,650, we have to find the factors of both numbers and list the highest common factor.

The factors of 213 are 1, 3, 71, 213

The factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650

The HCF of 213,650 is 1.

Lets's calculate GCF of 213,650

Greatest Common Factor (GCF) of 213,650 By Common Division

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

Greatest Common Factor of 213,650 By Matching Biggest Common Factor Method

Now, list down the factors of 213

1,3,71,213

Now, list down the factors of 650

1,2,5,10,13,25,26,50,65,130,325,650

Greatest Common Factor

We found the factors 213,650 . The biggest common factor number is the GCF number.
So the greatest common factor 213,650 is 1.

Lets's calculate LCM of 746,729

Lowest Common Multiple of 746,729 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 543834

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/543834

Therefore, the GCF of Fractions 213/746,650/729 is 1/543834

Least Common Multiple of 746,729 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 746,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(746,729) = 1

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

GCF(746,729) x common factors =1 x 1 = 1

LCM(746,729) = ( 746 × 729 ) / 1

LCM(746,729) = 543834 / 1

LCM(746,729) = 543834

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FAQs on GCF of Fractions of 213/746, 650/729

1. What is the HCF of 213,650?

The HCF of 213,650 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 213/746, 650/729?

Answer: GCF of Numerators as per given numbers 213/746, 650/729 is

GCF of Numerators i.e. for 213,650 is 1

LCM of denominators i.e. for 746,729 is 543834.

Thus, GCF of Fractions is 1/543834.Finally, GCF of Fractions for 213/746, 650/729 is 1/543834.