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GCF of 686/65, 224/206

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 686/65, 224/206 i.e 14/13390 easily. The following is the detailed procedure to determine the greatest common factor of fractions 686/65, 224/206.

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 686/65,224/206?

Given fractions are 686/65,224/206

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 686/65,224/206, numerators are 686,224

Denominators are 65,206

The GCF of 686,224 is 14 .

LCM of 65,206 is 13390.

The greatest common factor of 686/65,224/206 = [GCF of 686,224]/[LCM of 65,206]= 14/13390

Therefore, the GCF of 686/65,224/206 is 14/13390.

Greatest Common Factor of 686,224

To find the highest common factor of 686,224, we have to find the factors of both numbers and list the highest common factor.

The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686

The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224

The HCF of 686,224 is 14.

Lets's calculate GCF of 686,224

Greatest Common Factor (GCF) of 686,224 By Common Division

2 686, 224
7 343, 112
49, 16

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 686,224 By Matching Biggest Common Factor Method

Greatest Common Factor of 686,224 By Matching Biggest Common Factor Method

Now, list down the factors of 686

:

1,2,7,14,49,98,343,686

Now, list down the factors of 224

:

1,2,4,7,8,14,16,28,32,56,112,224

Greatest Common Factor

We found the factors 686,224 . The biggest common factor number is the GCF number.
So the greatest common factor 686,224 is 14.

Lets's calculate LCM of 65,206

Lowest Common Multiple of 65,206 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 13390

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/13390

Therefore, the GCF of Fractions 686/65,224/206 is 14/13390

Least Common Multiple of 65,206 with GCF Formula

Least Common Multiple of 65,206 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 65,206 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,206) = 1

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

GCF(65,206) x common factors =1 x 1 = 1

LCM(65,206) = ( 65 × 206 ) / 1

LCM(65,206) = 13390 / 1

LCM(65,206) = 13390


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FAQs on GCF of Fractions of 686/65, 224/206

1. What is the HCF of 686,224?

The HCF of 686,224 is 14

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 686/65, 224/206?

Answer: GCF of Numerators as per given numbers 686/65, 224/206 is

GCF of Numerators i.e. for 686,224 is 14

LCM of denominators i.e. for 65,206 is 13390.

Thus, GCF of Fractions is 14/13390.Finally, GCF of Fractions for 686/65, 224/206 is 14/13390.