How to Find GCF of 680/23, 204/6045?

GCF of 680/23, 204/6045

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 680/23, 204/6045 i.e 68/139035 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/23, 204/6045.

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 680/23,204/6045?

Given fractions are 680/23,204/6045

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 680/23,204/6045, numerators are 680,204

Denominators are 23,6045

The GCF of 680,204 is 68 .

LCM of 23,6045 is 139035.

The greatest common factor of 680/23,204/6045 = [GCF of 680,204]/[LCM of 23,6045]= 68/139035

Therefore, the GCF of 680/23,204/6045 is 68/139035.

Greatest Common Factor of 680,204

To find the highest common factor of 680,204, 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 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

The HCF of 680,204 is 68.

Lets's calculate GCF of 680,204

Greatest Common Factor (GCF) of 680,204 By Common Division

2	680, 204
2	340, 102
17	170, 51
	10, 3

∴ So the GCF of the given numbers is 2 x 2 x 17 = 68

Greatest Common Factor of 680,204 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 204

1,2,3,4,6,12,17,34,51,68,102,204

Greatest Common Factor

We found the factors 680,204 . The biggest common factor number is the GCF number.
So the greatest common factor 680,204 is 68.

Lets's calculate LCM of 23,6045

Lowest Common Multiple of 23,6045 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 139035

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 68/139035

Therefore, the GCF of Fractions 680/23,204/6045 is 68/139035

Least Common Multiple of 23,6045 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 23,6045 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,6045) = 1

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

GCF(23,6045) x common factors =1 x 1 = 1

LCM(23,6045) = ( 23 × 6045 ) / 1

LCM(23,6045) = 139035 / 1

LCM(23,6045) = 139035

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FAQs on GCF of Fractions of 680/23, 204/6045

1. What is the HCF of 680,204?

The HCF of 680,204 is 68

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 680/23, 204/6045?

Answer: GCF of Numerators as per given numbers 680/23, 204/6045 is

GCF of Numerators i.e. for 680,204 is 68

LCM of denominators i.e. for 23,6045 is 139035.

Thus, GCF of Fractions is 68/139035.Finally, GCF of Fractions for 680/23, 204/6045 is 68/139035.