How to Find GCF of 612/14, 978/2929?

GCF of 612/14, 978/2929

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 612/14, 978/2929 i.e 6/41006 easily. The following is the detailed procedure to determine the greatest common factor of fractions 612/14, 978/2929.

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 612/14,978/2929?

Given fractions are 612/14,978/2929

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 612/14,978/2929, numerators are 612,978

Denominators are 14,2929

The GCF of 612,978 is 6 .

LCM of 14,2929 is 41006.

The greatest common factor of 612/14,978/2929 = [GCF of 612,978]/[LCM of 14,2929]= 6/41006

Therefore, the GCF of 612/14,978/2929 is 6/41006.

Greatest Common Factor of 612,978

To find the highest common factor of 612,978, 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 978 are 1, 2, 3, 6, 163, 326, 489, 978

The HCF of 612,978 is 6.

Lets's calculate GCF of 612,978

Greatest Common Factor (GCF) of 612,978 By Common Division

2	612, 978
3	306, 489
	102, 163

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 612,978 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 978

1,2,3,6,163,326,489,978

Greatest Common Factor

We found the factors 612,978 . The biggest common factor number is the GCF number.
So the greatest common factor 612,978 is 6.

Lets's calculate LCM of 14,2929

Lowest Common Multiple of 14,2929 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 41006

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/41006

Therefore, the GCF of Fractions 612/14,978/2929 is 6/41006

Least Common Multiple of 14,2929 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 14,2929 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,2929) = 1

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

GCF(14,2929) x common factors =1 x 1 = 1

LCM(14,2929) = ( 14 × 2929 ) / 1

LCM(14,2929) = 41006 / 1

LCM(14,2929) = 41006

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FAQs on GCF of Fractions of 612/14, 978/2929

1. What is the HCF of 612,978?

The HCF of 612,978 is 6

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 612/14, 978/2929?

Answer: GCF of Numerators as per given numbers 612/14, 978/2929 is

GCF of Numerators i.e. for 612,978 is 6

LCM of denominators i.e. for 14,2929 is 41006.

Thus, GCF of Fractions is 6/41006.Finally, GCF of Fractions for 612/14, 978/2929 is 6/41006.