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GCF of 650/214, 7414/786

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 650/214, 7414/786 i.e 2/84102 easily. The following is the detailed procedure to determine the greatest common factor of fractions 650/214, 7414/786.

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 650/214,7414/786?

Given fractions are 650/214,7414/786

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 650/214,7414/786, numerators are 650,7414

Denominators are 214,786

The GCF of 650,7414 is 2 .

LCM of 214,786 is 84102.

The greatest common factor of 650/214,7414/786 = [GCF of 650,7414]/[LCM of 214,786]= 2/84102

Therefore, the GCF of 650/214,7414/786 is 2/84102.

Greatest Common Factor of 650,7414

To find the highest common factor of 650,7414, we have to find the factors of both numbers and list the highest common factor.

The factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650

The factors of 7414 are 1, 2, 11, 22, 337, 674, 3707, 7414

The HCF of 650,7414 is 2.

Lets's calculate GCF of 650,7414

Greatest Common Factor (GCF) of 650,7414 By Common Division

2 650, 7414
325, 3707

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

Greatest Common Factor of 650,7414 By Matching Biggest Common Factor Method

Greatest Common Factor of 650,7414 By Matching Biggest Common Factor Method

Now, list down the factors of 650

:

1,2,5,10,13,25,26,50,65,130,325,650

Now, list down the factors of 7414

:

1,2,11,22,337,674,3707,7414

Greatest Common Factor

We found the factors 650,7414 . The biggest common factor number is the GCF number.
So the greatest common factor 650,7414 is 2.

Lets's calculate LCM of 214,786

Lowest Common Multiple of 214,786 using Common Division

2 214, 786
107, 393

∴ So the LCM of the given numbers is 2 x 107 x 393 = 84102

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/84102

Therefore, the GCF of Fractions 650/214,7414/786 is 2/84102

Least Common Multiple of 214,786 with GCF Formula

Least Common Multiple of 214,786 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 214,786 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,786) = 2

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

GCF(214,786) x common factors =2 x 1 = 2

LCM(214,786) = ( 214 × 786 ) / 2

LCM(214,786) = 168204 / 2

LCM(214,786) = 84102


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FAQs on GCF of Fractions of 650/214, 7414/786

1. What is the HCF of 650,7414?

The HCF of 650,7414 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 650/214, 7414/786?

Answer: GCF of Numerators as per given numbers 650/214, 7414/786 is

GCF of Numerators i.e. for 650,7414 is 2

LCM of denominators i.e. for 214,786 is 84102.

Thus, GCF of Fractions is 2/84102.Finally, GCF of Fractions for 650/214, 7414/786 is 2/84102.