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GCF of 390/123, 232/314

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 390/123, 232/314 i.e 2/38622 easily. The following is the detailed procedure to determine the greatest common factor of fractions 390/123, 232/314.

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 390/123,232/314?

Given fractions are 390/123,232/314

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 390/123,232/314, numerators are 390,232

Denominators are 123,314

The GCF of 390,232 is 2 .

LCM of 123,314 is 38622.

The greatest common factor of 390/123,232/314 = [GCF of 390,232]/[LCM of 123,314]= 2/38622

Therefore, the GCF of 390/123,232/314 is 2/38622.

Greatest Common Factor of 390,232

To find the highest common factor of 390,232, we have to find the factors of both numbers and list the highest common factor.

The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390

The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232

The HCF of 390,232 is 2.

Lets's calculate GCF of 390,232

Greatest Common Factor (GCF) of 390,232 By Common Division

2 390, 232
195, 116

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 390,232 By Matching Biggest Common Factor Method

Greatest Common Factor of 390,232 By Matching Biggest Common Factor Method

Now, list down the factors of 390

:

1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390

Now, list down the factors of 232

:

1,2,4,8,29,58,116,232

Greatest Common Factor

We found the factors 390,232 . The biggest common factor number is the GCF number.
So the greatest common factor 390,232 is 2.

Lets's calculate LCM of 123,314

Lowest Common Multiple of 123,314 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 38622

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/38622

Therefore, the GCF of Fractions 390/123,232/314 is 2/38622

Least Common Multiple of 123,314 with GCF Formula

Least Common Multiple of 123,314 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 123,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(123,314) = 1

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

GCF(123,314) x common factors =1 x 1 = 1

LCM(123,314) = ( 123 × 314 ) / 1

LCM(123,314) = 38622 / 1

LCM(123,314) = 38622


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FAQs on GCF of Fractions of 390/123, 232/314

1. What is the HCF of 390,232?

The HCF of 390,232 is 2

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 390/123, 232/314?

Answer: GCF of Numerators as per given numbers 390/123, 232/314 is

GCF of Numerators i.e. for 390,232 is 2

LCM of denominators i.e. for 123,314 is 38622.

Thus, GCF of Fractions is 2/38622.Finally, GCF of Fractions for 390/123, 232/314 is 2/38622.