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GCF of 310/52, 430/565

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 310/52, 430/565 i.e 10/29380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 310/52, 430/565.

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 310/52,430/565?

Given fractions are 310/52,430/565

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 310/52,430/565, numerators are 310,430

Denominators are 52,565

The GCF of 310,430 is 10 .

LCM of 52,565 is 29380.

The greatest common factor of 310/52,430/565 = [GCF of 310,430]/[LCM of 52,565]= 10/29380

Therefore, the GCF of 310/52,430/565 is 10/29380.

Greatest Common Factor of 310,430

To find the highest common factor of 310,430, we have to find the factors of both numbers and list the highest common factor.

The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310

The factors of 430 are 1, 2, 5, 10, 43, 86, 215, 430

The HCF of 310,430 is 10.

Lets's calculate GCF of 310,430

Greatest Common Factor (GCF) of 310,430 By Common Division

2 310, 430
5 155, 215
31, 43

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

Greatest Common Factor of 310,430 By Matching Biggest Common Factor Method

Greatest Common Factor of 310,430 By Matching Biggest Common Factor Method

Now, list down the factors of 310

:

1,2,5,10,31,62,155,310

Now, list down the factors of 430

:

1,2,5,10,43,86,215,430

Greatest Common Factor

We found the factors 310,430 . The biggest common factor number is the GCF number.
So the greatest common factor 310,430 is 10.

Lets's calculate LCM of 52,565

Lowest Common Multiple of 52,565 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 29380

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/29380

Therefore, the GCF of Fractions 310/52,430/565 is 10/29380

Least Common Multiple of 52,565 with GCF Formula

Least Common Multiple of 52,565 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 52,565 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(52,565) = 1

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

GCF(52,565) x common factors =1 x 1 = 1

LCM(52,565) = ( 52 × 565 ) / 1

LCM(52,565) = 29380 / 1

LCM(52,565) = 29380


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FAQs on GCF of Fractions of 310/52, 430/565

1. What is the HCF of 310,430?

The HCF of 310,430 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 310/52, 430/565?

Answer: GCF of Numerators as per given numbers 310/52, 430/565 is

GCF of Numerators i.e. for 310,430 is 10

LCM of denominators i.e. for 52,565 is 29380.

Thus, GCF of Fractions is 10/29380.Finally, GCF of Fractions for 310/52, 430/565 is 10/29380.