How to Find GCF of 204/390, 700/382?

GCF of 204/390, 700/382

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 204/390, 700/382 i.e 4/74490 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/390, 700/382.

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 204/390,700/382?

Given fractions are 204/390,700/382

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 204/390,700/382, numerators are 204,700

Denominators are 390,382

The GCF of 204,700 is 4 .

LCM of 390,382 is 74490.

The greatest common factor of 204/390,700/382 = [GCF of 204,700]/[LCM of 390,382]= 4/74490

Therefore, the GCF of 204/390,700/382 is 4/74490.

Greatest Common Factor of 204,700

To find the highest common factor of 204,700, we have to find the factors of both numbers and list the highest common factor.

The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204

The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700

The HCF of 204,700 is 4.

Lets's calculate GCF of 204,700

Greatest Common Factor (GCF) of 204,700 By Common Division

2	204, 700
2	102, 350
	51, 175

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 204,700 By Matching Biggest Common Factor Method

Now, list down the factors of 204

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

Now, list down the factors of 700

1,2,4,5,7,10,14,20,25,28,35,50,70,100,140,175,350,700

Greatest Common Factor

We found the factors 204,700 . The biggest common factor number is the GCF number.
So the greatest common factor 204,700 is 4.

Lets's calculate LCM of 390,382

Lowest Common Multiple of 390,382 using Common Division

2	390, 382
	195, 191

∴ So the LCM of the given numbers is 2 x 195 x 191 = 74490

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/74490

Therefore, the GCF of Fractions 204/390,700/382 is 4/74490

Least Common Multiple of 390,382 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 390,382 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(390,382) = 2

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

GCF(390,382) x common factors =2 x 1 = 2

LCM(390,382) = ( 390 × 382 ) / 2

LCM(390,382) = 148980 / 2

LCM(390,382) = 74490

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 204/390, 700/382

1. What is the HCF of 204,700?

The HCF of 204,700 is 4

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 204/390, 700/382?

Answer: GCF of Numerators as per given numbers 204/390, 700/382 is

GCF of Numerators i.e. for 204,700 is 4

LCM of denominators i.e. for 390,382 is 74490.

Thus, GCF of Fractions is 4/74490.Finally, GCF of Fractions for 204/390, 700/382 is 4/74490.