How to Find GCF of 697/512, 6562/7054?

GCF of 697/512, 6562/7054

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 697/512, 6562/7054 i.e 17/1805824 easily. The following is the detailed procedure to determine the greatest common factor of fractions 697/512, 6562/7054.

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 697/512,6562/7054?

Given fractions are 697/512,6562/7054

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 697/512,6562/7054, numerators are 697,6562

Denominators are 512,7054

The GCF of 697,6562 is 17 .

LCM of 512,7054 is 1805824.

The greatest common factor of 697/512,6562/7054 = [GCF of 697,6562]/[LCM of 512,7054]= 17/1805824

Therefore, the GCF of 697/512,6562/7054 is 17/1805824.

Greatest Common Factor of 697,6562

To find the highest common factor of 697,6562, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 6562 are 1, 2, 17, 34, 193, 386, 3281, 6562

The HCF of 697,6562 is 17.

Lets's calculate GCF of 697,6562

Greatest Common Factor (GCF) of 697,6562 By Common Division

17	697, 6562
	41, 386

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

Greatest Common Factor of 697,6562 By Matching Biggest Common Factor Method

Now, list down the factors of 697

1,17,41,697

Now, list down the factors of 6562

1,2,17,34,193,386,3281,6562

Greatest Common Factor

We found the factors 697,6562 . The biggest common factor number is the GCF number.
So the greatest common factor 697,6562 is 17.

Lets's calculate LCM of 512,7054

Lowest Common Multiple of 512,7054 using Common Division

2	512, 7054
	256, 3527

∴ So the LCM of the given numbers is 2 x 256 x 3527 = 1805824

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/1805824

Therefore, the GCF of Fractions 697/512,6562/7054 is 17/1805824

Least Common Multiple of 512,7054 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 512,7054 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(512,7054) = 2

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

GCF(512,7054) x common factors =2 x 1 = 2

LCM(512,7054) = ( 512 × 7054 ) / 2

LCM(512,7054) = 3611648 / 2

LCM(512,7054) = 1805824

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FAQs on GCF of Fractions of 697/512, 6562/7054

1. What is the HCF of 697,6562?

The HCF of 697,6562 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 697/512, 6562/7054?

Answer: GCF of Numerators as per given numbers 697/512, 6562/7054 is

GCF of Numerators i.e. for 697,6562 is 17

LCM of denominators i.e. for 512,7054 is 1805824.

Thus, GCF of Fractions is 17/1805824.Finally, GCF of Fractions for 697/512, 6562/7054 is 17/1805824.