How to Find GCF of 646/684, 697/217?

GCF of 646/684, 697/217

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 646/684, 697/217 i.e 17/148428 easily. The following is the detailed procedure to determine the greatest common factor of fractions 646/684, 697/217.

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 646/684,697/217?

Given fractions are 646/684,697/217

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 646/684,697/217, numerators are 646,697

Denominators are 684,217

The GCF of 646,697 is 17 .

LCM of 684,217 is 148428.

The greatest common factor of 646/684,697/217 = [GCF of 646,697]/[LCM of 684,217]= 17/148428

Therefore, the GCF of 646/684,697/217 is 17/148428.

Greatest Common Factor of 646,697

To find the highest common factor of 646,697, we have to find the factors of both numbers and list the highest common factor.

The factors of 646 are 1, 2, 17, 19, 34, 38, 323, 646

The factors of 697 are 1, 17, 41, 697

The HCF of 646,697 is 17.

Lets's calculate GCF of 646,697

Greatest Common Factor (GCF) of 646,697 By Common Division

17	646, 697
	38, 41

∴ So the GCF of the given numbers is 17 = 17

Greatest Common Factor of 646,697 By Matching Biggest Common Factor Method

Now, list down the factors of 646

1,2,17,19,34,38,323,646

Now, list down the factors of 697

1,17,41,697

Greatest Common Factor

We found the factors 646,697 . The biggest common factor number is the GCF number.
So the greatest common factor 646,697 is 17.

Lets's calculate LCM of 684,217

Lowest Common Multiple of 684,217 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 148428

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/148428

Therefore, the GCF of Fractions 646/684,697/217 is 17/148428

Least Common Multiple of 684,217 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 684,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(684,217) = 1

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

GCF(684,217) x common factors =1 x 1 = 1

LCM(684,217) = ( 684 × 217 ) / 1

LCM(684,217) = 148428 / 1

LCM(684,217) = 148428

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FAQs on GCF of Fractions of 646/684, 697/217

1. What is the HCF of 646,697?

The HCF of 646,697 is 17

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 646/684, 697/217?

Answer: GCF of Numerators as per given numbers 646/684, 697/217 is

GCF of Numerators i.e. for 646,697 is 17

LCM of denominators i.e. for 684,217 is 148428.

Thus, GCF of Fractions is 17/148428.Finally, GCF of Fractions for 646/684, 697/217 is 17/148428.