How to Find GCF of 230/404, 770/763?

GCF of 230/404, 770/763

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 230/404, 770/763 i.e 10/308252 easily. The following is the detailed procedure to determine the greatest common factor of fractions 230/404, 770/763.

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 230/404,770/763?

Given fractions are 230/404,770/763

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 230/404,770/763, numerators are 230,770

Denominators are 404,763

The GCF of 230,770 is 10 .

LCM of 404,763 is 308252.

The greatest common factor of 230/404,770/763 = [GCF of 230,770]/[LCM of 404,763]= 10/308252

Therefore, the GCF of 230/404,770/763 is 10/308252.

Greatest Common Factor of 230,770

To find the highest common factor of 230,770, we have to find the factors of both numbers and list the highest common factor.

The factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230

The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770

The HCF of 230,770 is 10.

Lets's calculate GCF of 230,770

Greatest Common Factor (GCF) of 230,770 By Common Division

2	230, 770
5	115, 385
	23, 77

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 230,770 By Matching Biggest Common Factor Method

Now, list down the factors of 230

1,2,5,10,23,46,115,230

Now, list down the factors of 770

1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770

Greatest Common Factor

We found the factors 230,770 . The biggest common factor number is the GCF number.
So the greatest common factor 230,770 is 10.

Lets's calculate LCM of 404,763

Lowest Common Multiple of 404,763 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 308252

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/308252

Therefore, the GCF of Fractions 230/404,770/763 is 10/308252

Least Common Multiple of 404,763 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 404,763 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(404,763) = 1

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

GCF(404,763) x common factors =1 x 1 = 1

LCM(404,763) = ( 404 × 763 ) / 1

LCM(404,763) = 308252 / 1

LCM(404,763) = 308252

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FAQs on GCF of Fractions of 230/404, 770/763

1. What is the HCF of 230,770?

The HCF of 230,770 is 10

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 230/404, 770/763?

Answer: GCF of Numerators as per given numbers 230/404, 770/763 is

GCF of Numerators i.e. for 230,770 is 10

LCM of denominators i.e. for 404,763 is 308252.

Thus, GCF of Fractions is 10/308252.Finally, GCF of Fractions for 230/404, 770/763 is 10/308252.