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GCF of 365/123, 570/460

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 365/123, 570/460 i.e 5/56580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 365/123, 570/460.

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 365/123,570/460?

Given fractions are 365/123,570/460

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 365/123,570/460, numerators are 365,570

Denominators are 123,460

The GCF of 365,570 is 5 .

LCM of 123,460 is 56580.

The greatest common factor of 365/123,570/460 = [GCF of 365,570]/[LCM of 123,460]= 5/56580

Therefore, the GCF of 365/123,570/460 is 5/56580.

Greatest Common Factor of 365,570

To find the highest common factor of 365,570, we have to find the factors of both numbers and list the highest common factor.

The factors of 365 are 1, 5, 73, 365

The factors of 570 are 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570

The HCF of 365,570 is 5.

Lets's calculate GCF of 365,570

Greatest Common Factor (GCF) of 365,570 By Common Division

5 365, 570
73, 114

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 365,570 By Matching Biggest Common Factor Method

Greatest Common Factor of 365,570 By Matching Biggest Common Factor Method

Now, list down the factors of 365

:

1,5,73,365

Now, list down the factors of 570

:

1,2,3,5,6,10,15,19,30,38,57,95,114,190,285,570

Greatest Common Factor

We found the factors 365,570 . The biggest common factor number is the GCF number.
So the greatest common factor 365,570 is 5.

Lets's calculate LCM of 123,460

Lowest Common Multiple of 123,460 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 56580

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/56580

Therefore, the GCF of Fractions 365/123,570/460 is 5/56580

Least Common Multiple of 123,460 with GCF Formula

Least Common Multiple of 123,460 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 123,460 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(123,460) = 1

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

GCF(123,460) x common factors =1 x 1 = 1

LCM(123,460) = ( 123 × 460 ) / 1

LCM(123,460) = 56580 / 1

LCM(123,460) = 56580


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FAQs on GCF of Fractions of 365/123, 570/460

1. What is the HCF of 365,570?

The HCF of 365,570 is 5

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 365/123, 570/460?

Answer: GCF of Numerators as per given numbers 365/123, 570/460 is

GCF of Numerators i.e. for 365,570 is 5

LCM of denominators i.e. for 123,460 is 56580.

Thus, GCF of Fractions is 5/56580.Finally, GCF of Fractions for 365/123, 570/460 is 5/56580.