How to Find GCF of 680/77, 400/7397?

GCF of 680/77, 400/7397

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 680/77, 400/7397 i.e 40/569569 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/77, 400/7397.

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 680/77,400/7397?

Given fractions are 680/77,400/7397

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 680/77,400/7397, numerators are 680,400

Denominators are 77,7397

The GCF of 680,400 is 40 .

LCM of 77,7397 is 569569.

The greatest common factor of 680/77,400/7397 = [GCF of 680,400]/[LCM of 77,7397]= 40/569569

Therefore, the GCF of 680/77,400/7397 is 40/569569.

Greatest Common Factor of 680,400

To find the highest common factor of 680,400, we have to find the factors of both numbers and list the highest common factor.

The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680

The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

The HCF of 680,400 is 40.

Lets's calculate GCF of 680,400

Greatest Common Factor (GCF) of 680,400 By Common Division

2	680, 400
2	340, 200
2	170, 100
5	85, 50
	17, 10

∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40

Greatest Common Factor of 680,400 By Matching Biggest Common Factor Method

Now, list down the factors of 680

1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680

Now, list down the factors of 400

1,2,4,5,8,10,16,20,25,40,50,80,100,200,400

Greatest Common Factor

We found the factors 680,400 . The biggest common factor number is the GCF number.
So the greatest common factor 680,400 is 40.

Lets's calculate LCM of 77,7397

Lowest Common Multiple of 77,7397 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 569569

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/569569

Therefore, the GCF of Fractions 680/77,400/7397 is 40/569569

Least Common Multiple of 77,7397 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 77,7397 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(77,7397) = 1

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

GCF(77,7397) x common factors =1 x 1 = 1

LCM(77,7397) = ( 77 × 7397 ) / 1

LCM(77,7397) = 569569 / 1

LCM(77,7397) = 569569

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FAQs on GCF of Fractions of 680/77, 400/7397

1. What is the HCF of 680,400?

The HCF of 680,400 is 40

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 680/77, 400/7397?

Answer: GCF of Numerators as per given numbers 680/77, 400/7397 is

GCF of Numerators i.e. for 680,400 is 40

LCM of denominators i.e. for 77,7397 is 569569.

Thus, GCF of Fractions is 40/569569.Finally, GCF of Fractions for 680/77, 400/7397 is 40/569569.