How to Find GCF of 612/76, 924/721?

GCF of 612/76, 924/721

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 612/76, 924/721 i.e 12/54796 easily. The following is the detailed procedure to determine the greatest common factor of fractions 612/76, 924/721.

Enter two or more fractions separated by "commas"

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

What is the GCF of 612/76,924/721?

Given fractions are 612/76,924/721

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 612/76,924/721, numerators are 612,924

Denominators are 76,721

The GCF of 612,924 is 12 .

LCM of 76,721 is 54796.

The greatest common factor of 612/76,924/721 = [GCF of 612,924]/[LCM of 76,721]= 12/54796

Therefore, the GCF of 612/76,924/721 is 12/54796.

Greatest Common Factor of 612,924

To find the highest common factor of 612,924, 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 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924

The HCF of 612,924 is 12.

Lets's calculate GCF of 612,924

Greatest Common Factor (GCF) of 612,924 By Common Division

2	612, 924
2	306, 462
3	153, 231
	51, 77

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 612,924 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 924

1,2,3,4,6,7,11,12,14,21,22,28,33,42,44,66,77,84,132,154,231,308,462,924

Greatest Common Factor

We found the factors 612,924 . The biggest common factor number is the GCF number.
So the greatest common factor 612,924 is 12.

Lets's calculate LCM of 76,721

Lowest Common Multiple of 76,721 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 54796

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/54796

Therefore, the GCF of Fractions 612/76,924/721 is 12/54796

Least Common Multiple of 76,721 with GCF Formula

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

We need to calculate greatest common factor of 76,721 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,721) = 1

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

GCF(76,721) x common factors =1 x 1 = 1

LCM(76,721) = ( 76 × 721 ) / 1

LCM(76,721) = 54796 / 1

LCM(76,721) = 54796

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FAQs on GCF of Fractions of 612/76, 924/721

1. What is the HCF of 612,924?

The HCF of 612,924 is 12

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 612/76, 924/721?

Answer: GCF of Numerators as per given numbers 612/76, 924/721 is

GCF of Numerators i.e. for 612,924 is 12

LCM of denominators i.e. for 76,721 is 54796.

Thus, GCF of Fractions is 12/54796.Finally, GCF of Fractions for 612/76, 924/721 is 12/54796.