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GCF of 614/87, 658/104

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 614/87, 658/104 i.e 2/9048 easily. The following is the detailed procedure to determine the greatest common factor of fractions 614/87, 658/104.

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 614/87,658/104?

Given fractions are 614/87,658/104

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 614/87,658/104, numerators are 614,658

Denominators are 87,104

The GCF of 614,658 is 2 .

LCM of 87,104 is 9048.

The greatest common factor of 614/87,658/104 = [GCF of 614,658]/[LCM of 87,104]= 2/9048

Therefore, the GCF of 614/87,658/104 is 2/9048.

Greatest Common Factor of 614,658

To find the highest common factor of 614,658, we have to find the factors of both numbers and list the highest common factor.

The factors of 614 are 1, 2, 307, 614

The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658

The HCF of 614,658 is 2.

Lets's calculate GCF of 614,658

Greatest Common Factor (GCF) of 614,658 By Common Division

2 614, 658
307, 329

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 614,658 By Matching Biggest Common Factor Method

Greatest Common Factor of 614,658 By Matching Biggest Common Factor Method

Now, list down the factors of 614

:

1,2,307,614

Now, list down the factors of 658

:

1,2,7,14,47,94,329,658

Greatest Common Factor

We found the factors 614,658 . The biggest common factor number is the GCF number.
So the greatest common factor 614,658 is 2.

Lets's calculate LCM of 87,104

Lowest Common Multiple of 87,104 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9048

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/9048

Therefore, the GCF of Fractions 614/87,658/104 is 2/9048

Least Common Multiple of 87,104 with GCF Formula

Least Common Multiple of 87,104 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 87,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(87,104) = 1

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

GCF(87,104) x common factors =1 x 1 = 1

LCM(87,104) = ( 87 × 104 ) / 1

LCM(87,104) = 9048 / 1

LCM(87,104) = 9048


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FAQs on GCF of Fractions of 614/87, 658/104

1. What is the HCF of 614,658?

The HCF of 614,658 is 2

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 614/87, 658/104?

Answer: GCF of Numerators as per given numbers 614/87, 658/104 is

GCF of Numerators i.e. for 614,658 is 2

LCM of denominators i.e. for 87,104 is 9048.

Thus, GCF of Fractions is 2/9048.Finally, GCF of Fractions for 614/87, 658/104 is 2/9048.