How to Find GCF of 678/223, 697/730?

GCF of 678/223, 697/730

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 678/223, 697/730 i.e 1/162790 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/223, 697/730.

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 678/223,697/730?

Given fractions are 678/223,697/730

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 678/223,697/730, numerators are 678,697

Denominators are 223,730

The GCF of 678,697 is 1 .

LCM of 223,730 is 162790.

The greatest common factor of 678/223,697/730 = [GCF of 678,697]/[LCM of 223,730]= 1/162790

Therefore, the GCF of 678/223,697/730 is 1/162790.

Greatest Common Factor of 678,697

To find the highest common factor of 678,697, we have to find the factors of both numbers and list the highest common factor.

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

The factors of 697 are 1, 17, 41, 697

The HCF of 678,697 is 1.

Lets's calculate GCF of 678,697

Greatest Common Factor (GCF) of 678,697 By Common Division

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

Greatest Common Factor of 678,697 By Matching Biggest Common Factor Method

Now, list down the factors of 678

1,2,3,6,113,226,339,678

Now, list down the factors of 697

1,17,41,697

Greatest Common Factor

We found the factors 678,697 . The biggest common factor number is the GCF number.
So the greatest common factor 678,697 is 1.

Lets's calculate LCM of 223,730

Lowest Common Multiple of 223,730 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 162790

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/162790

Therefore, the GCF of Fractions 678/223,697/730 is 1/162790

Least Common Multiple of 223,730 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 223,730 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(223,730) = 1

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

GCF(223,730) x common factors =1 x 1 = 1

LCM(223,730) = ( 223 × 730 ) / 1

LCM(223,730) = 162790 / 1

LCM(223,730) = 162790

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 678/223, 697/730

1. What is the HCF of 678,697?

The HCF of 678,697 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 678/223, 697/730?

Answer: GCF of Numerators as per given numbers 678/223, 697/730 is

GCF of Numerators i.e. for 678,697 is 1

LCM of denominators i.e. for 223,730 is 162790.

Thus, GCF of Fractions is 1/162790.Finally, GCF of Fractions for 678/223, 697/730 is 1/162790.