How to Find GCF of 609/22, 856/74, 314/57?

GCF of 609/22, 856/74, 314/57

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 609/22, 856/74, 314/57 i.e 1/46398 easily. The following is the detailed procedure to determine the greatest common factor of fractions 609/22, 856/74, 314/57.

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 609/22,856/74,314/57?

Given fractions are 609/22,856/74,314/57

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 609/22,856/74,314/57, numerators are 609,856,314

Denominators are 22,74,57

The GCF of 609,856,314 is 1 .

LCM of 22,74,57 is 46398.

The greatest common factor of 609/22,856/74,314/57 = [GCF of 609,856,314]/[LCM of 22,74,57]= 1/46398

Therefore, the GCF of 609/22,856/74,314/57 is 1/46398.

Greatest Common Factor of 609,856,314

To find the highest common factor of 609,856,314, we have to find the factors of both numbers and list the highest common factor.

The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609

The factors of 856 are 1, 2, 4, 8, 107, 214, 428, 856

The factors of 314 are 1, 2, 157, 314

The HCF of 609,856,314 is 1.

Lets's calculate GCF of 609,856,314

Greatest Common Factor (GCF) of 609,856,314 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 609,856,314 By Matching Biggest Common Factor Method

Now, list down the factors of 609

1,3,7,21,29,87,203,609

Now, list down the factors of 856

1,2,4,8,107,214,428,856

Now, list down the factors of 314

1,2,157,314

Greatest Common Factor

We found the factors 609,856,314 . The biggest common factor number is the GCF number.
So the greatest common factor 609,856,314 is 1.

Lets's calculate LCM of 22,74,57

Lowest Common Multiple of 22,74,57 using Common Division

2	22, 74, 57
	11, 37, 57

∴ So the LCM of the given numbers is 2 x 11 x 37 x 57 = 46398

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/46398

Therefore, the GCF of Fractions 609/22,856/74,314/57 is 1/46398

Least Common Multiple of 22,74,57 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 22,74,57 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(22,74,57) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(22,74,57) x common factors =1 x 2 = 2

LCM(22,74,57) = ( 22 × 74 × 57 ) / 2

LCM(22,74,57) = 92796 / 2

LCM(22,74,57) = 46398

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FAQs on GCF of Fractions of 609/22, 856/74, 314/57

1. What is the HCF of 609,856,314?

The HCF of 609,856,314 is 1

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 609/22, 856/74, 314/57?

Answer: GCF of Numerators as per given numbers 609/22, 856/74, 314/57 is

GCF of Numerators i.e. for 609,856,314 is 1

LCM of denominators i.e. for 22,74,57 is 46398.

Thus, GCF of Fractions is 1/46398.Finally, GCF of Fractions for 609/22, 856/74, 314/57 is 1/46398.