How to Find GCF of 852/258, 3714/619?

GCF of 852/258, 3714/619

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 852/258, 3714/619 i.e 6/159702 easily. The following is the detailed procedure to determine the greatest common factor of fractions 852/258, 3714/619.

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 852/258,3714/619?

Given fractions are 852/258,3714/619

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 852/258,3714/619, numerators are 852,3714

Denominators are 258,619

The GCF of 852,3714 is 6 .

LCM of 258,619 is 159702.

The greatest common factor of 852/258,3714/619 = [GCF of 852,3714]/[LCM of 258,619]= 6/159702

Therefore, the GCF of 852/258,3714/619 is 6/159702.

Greatest Common Factor of 852,3714

To find the highest common factor of 852,3714, we have to find the factors of both numbers and list the highest common factor.

The factors of 852 are 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852

The factors of 3714 are 1, 2, 3, 6, 619, 1238, 1857, 3714

The HCF of 852,3714 is 6.

Lets's calculate GCF of 852,3714

Greatest Common Factor (GCF) of 852,3714 By Common Division

2	852, 3714
3	426, 1857
	142, 619

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

Greatest Common Factor of 852,3714 By Matching Biggest Common Factor Method

Now, list down the factors of 852

1,2,3,4,6,12,71,142,213,284,426,852

Now, list down the factors of 3714

1,2,3,6,619,1238,1857,3714

Greatest Common Factor

We found the factors 852,3714 . The biggest common factor number is the GCF number.
So the greatest common factor 852,3714 is 6.

Lets's calculate LCM of 258,619

Lowest Common Multiple of 258,619 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 159702

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/159702

Therefore, the GCF of Fractions 852/258,3714/619 is 6/159702

Least Common Multiple of 258,619 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 258,619 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(258,619) = 1

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

GCF(258,619) x common factors =1 x 1 = 1

LCM(258,619) = ( 258 × 619 ) / 1

LCM(258,619) = 159702 / 1

LCM(258,619) = 159702

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FAQs on GCF of Fractions of 852/258, 3714/619

1. What is the HCF of 852,3714?

The HCF of 852,3714 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 852/258, 3714/619?

Answer: GCF of Numerators as per given numbers 852/258, 3714/619 is

GCF of Numerators i.e. for 852,3714 is 6

LCM of denominators i.e. for 258,619 is 159702.

Thus, GCF of Fractions is 6/159702.Finally, GCF of Fractions for 852/258, 3714/619 is 6/159702.