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GCF of 270/446, 765/386

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 270/446, 765/386 i.e 45/86078 easily. The following is the detailed procedure to determine the greatest common factor of fractions 270/446, 765/386.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 270/446,765/386?

Given fractions are 270/446,765/386

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 270/446,765/386, numerators are 270,765

Denominators are 446,386

The GCF of 270,765 is 45 .

LCM of 446,386 is 86078.

The greatest common factor of 270/446,765/386 = [GCF of 270,765]/[LCM of 446,386]= 45/86078

Therefore, the GCF of 270/446,765/386 is 45/86078.

Greatest Common Factor of 270,765

To find the highest common factor of 270,765, we have to find the factors of both numbers and list the highest common factor.

The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270

The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765

The HCF of 270,765 is 45.

Lets's calculate GCF of 270,765

Greatest Common Factor (GCF) of 270,765 By Common Division

3 270, 765
3 90, 255
5 30, 85
6, 17

∴ So the GCF of the given numbers is 3 x 3 x 5 = 45

Greatest Common Factor of 270,765 By Matching Biggest Common Factor Method

Greatest Common Factor of 270,765 By Matching Biggest Common Factor Method

Now, list down the factors of 270

:

1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270

Now, list down the factors of 765

:

1,3,5,9,15,17,45,51,85,153,255,765

Greatest Common Factor

We found the factors 270,765 . The biggest common factor number is the GCF number.
So the greatest common factor 270,765 is 45.


Lets's calculate LCM of 446,386

Lowest Common Multiple of 446,386 using Common Division

2 446, 386
223, 193

∴ So the LCM of the given numbers is 2 x 223 x 193 = 86078

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/86078

Therefore, the GCF of Fractions 270/446,765/386 is 45/86078

Least Common Multiple of 446,386 with GCF Formula

Least Common Multiple of 446,386 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 446,386 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(446,386) = 2

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

GCF(446,386) x common factors =2 x 1 = 2

LCM(446,386) = ( 446 × 386 ) / 2

LCM(446,386) = 172156 / 2

LCM(446,386) = 86078


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 270/446, 765/386

1. What is the HCF of 270,765?

The HCF of 270,765 is 45

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 270/446, 765/386?

Answer: GCF of Numerators as per given numbers 270/446, 765/386 is

GCF of Numerators i.e. for 270,765 is 45

LCM of denominators i.e. for 446,386 is 86078.

Thus, GCF of Fractions is 45/86078.Finally, GCF of Fractions for 270/446, 765/386 is 45/86078.