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GCF of 612/30, 538/568

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 612/30, 538/568 i.e 2/8520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 612/30, 538/568.

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 612/30,538/568?

Given fractions are 612/30,538/568

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 612/30,538/568, numerators are 612,538

Denominators are 30,568

The GCF of 612,538 is 2 .

LCM of 30,568 is 8520.

The greatest common factor of 612/30,538/568 = [GCF of 612,538]/[LCM of 30,568]= 2/8520

Therefore, the GCF of 612/30,538/568 is 2/8520.

Greatest Common Factor of 612,538

To find the highest common factor of 612,538, we have to find the factors of both numbers and list the highest common factor.

The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612

The factors of 538 are 1, 2, 269, 538

The HCF of 612,538 is 2.

Lets's calculate GCF of 612,538

Greatest Common Factor (GCF) of 612,538 By Common Division

2 612, 538
306, 269

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

Greatest Common Factor of 612,538 By Matching Biggest Common Factor Method

Greatest Common Factor of 612,538 By Matching Biggest Common Factor Method

Now, list down the factors of 612

:

1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612

Now, list down the factors of 538

:

1,2,269,538

Greatest Common Factor

We found the factors 612,538 . The biggest common factor number is the GCF number.
So the greatest common factor 612,538 is 2.

Lets's calculate LCM of 30,568

Lowest Common Multiple of 30,568 using Common Division

2 30, 568
15, 284

∴ So the LCM of the given numbers is 2 x 15 x 284 = 8520

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8520

Therefore, the GCF of Fractions 612/30,538/568 is 2/8520

Least Common Multiple of 30,568 with GCF Formula

Least Common Multiple of 30,568 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 30,568 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,568) = 2

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

GCF(30,568) x common factors =2 x 1 = 2

LCM(30,568) = ( 30 × 568 ) / 2

LCM(30,568) = 17040 / 2

LCM(30,568) = 8520


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FAQs on GCF of Fractions of 612/30, 538/568

1. What is the HCF of 612,538?

The HCF of 612,538 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 612/30, 538/568?

Answer: GCF of Numerators as per given numbers 612/30, 538/568 is

GCF of Numerators i.e. for 612,538 is 2

LCM of denominators i.e. for 30,568 is 8520.

Thus, GCF of Fractions is 2/8520.Finally, GCF of Fractions for 612/30, 538/568 is 2/8520.