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GCF of 19/614, 57/706

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 19/614, 57/706 i.e 19/216742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 19/614, 57/706.

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 19/614,57/706?

Given fractions are 19/614,57/706

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 19/614,57/706, numerators are 19,57

Denominators are 614,706

The GCF of 19,57 is 19 .

LCM of 614,706 is 216742.

The greatest common factor of 19/614,57/706 = [GCF of 19,57]/[LCM of 614,706]= 19/216742

Therefore, the GCF of 19/614,57/706 is 19/216742.

Greatest Common Factor of 19,57

To find the highest common factor of 19,57, we have to find the factors of both numbers and list the highest common factor.

The factors of 19 are 1, 19

The factors of 57 are 1, 3, 19, 57

The HCF of 19,57 is 19.

Lets's calculate GCF of 19,57

Greatest Common Factor (GCF) of 19,57 By Common Division

19 19, 57
1, 3

∴ So the GCF of the given numbers is 19 = 19

Greatest Common Factor of 19,57 By Matching Biggest Common Factor Method

Greatest Common Factor of 19,57 By Matching Biggest Common Factor Method

Now, list down the factors of 19

:

1,19

Now, list down the factors of 57

:

1,3,19,57

Greatest Common Factor

We found the factors 19,57 . The biggest common factor number is the GCF number.
So the greatest common factor 19,57 is 19.

Lets's calculate LCM of 614,706

Lowest Common Multiple of 614,706 using Common Division

2 614, 706
307, 353

∴ So the LCM of the given numbers is 2 x 307 x 353 = 216742

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/216742

Therefore, the GCF of Fractions 19/614,57/706 is 19/216742

Least Common Multiple of 614,706 with GCF Formula

Least Common Multiple of 614,706 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 614,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(614,706) = 2

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

GCF(614,706) x common factors =2 x 1 = 2

LCM(614,706) = ( 614 × 706 ) / 2

LCM(614,706) = 433484 / 2

LCM(614,706) = 216742


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FAQs on GCF of Fractions of 19/614, 57/706

1. What is the HCF of 19,57?

The HCF of 19,57 is 19

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 19/614, 57/706?

Answer: GCF of Numerators as per given numbers 19/614, 57/706 is

GCF of Numerators i.e. for 19,57 is 19

LCM of denominators i.e. for 614,706 is 216742.

Thus, GCF of Fractions is 19/216742.Finally, GCF of Fractions for 19/614, 57/706 is 19/216742.