How to Find GCF of 294/490, 402/419?

GCF of 294/490, 402/419

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 294/490, 402/419 i.e 6/205310 easily. The following is the detailed procedure to determine the greatest common factor of fractions 294/490, 402/419.

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 294/490,402/419?

Given fractions are 294/490,402/419

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 294/490,402/419, numerators are 294,402

Denominators are 490,419

The GCF of 294,402 is 6 .

LCM of 490,419 is 205310.

The greatest common factor of 294/490,402/419 = [GCF of 294,402]/[LCM of 490,419]= 6/205310

Therefore, the GCF of 294/490,402/419 is 6/205310.

Greatest Common Factor of 294,402

To find the highest common factor of 294,402, we have to find the factors of both numbers and list the highest common factor.

The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294

The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402

The HCF of 294,402 is 6.

Lets's calculate GCF of 294,402

Greatest Common Factor (GCF) of 294,402 By Common Division

2	294, 402
3	147, 201
	49, 67

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 294,402 By Matching Biggest Common Factor Method

Now, list down the factors of 294

1,2,3,6,7,14,21,42,49,98,147,294

Now, list down the factors of 402

1,2,3,6,67,134,201,402

Greatest Common Factor

We found the factors 294,402 . The biggest common factor number is the GCF number.
So the greatest common factor 294,402 is 6.

Lets's calculate LCM of 490,419

Lowest Common Multiple of 490,419 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 205310

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/205310

Therefore, the GCF of Fractions 294/490,402/419 is 6/205310

Least Common Multiple of 490,419 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 490,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(490,419) = 1

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

GCF(490,419) x common factors =1 x 1 = 1

LCM(490,419) = ( 490 × 419 ) / 1

LCM(490,419) = 205310 / 1

LCM(490,419) = 205310

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FAQs on GCF of Fractions of 294/490, 402/419

1. What is the HCF of 294,402?

The HCF of 294,402 is 6

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 294/490, 402/419?

Answer: GCF of Numerators as per given numbers 294/490, 402/419 is

GCF of Numerators i.e. for 294,402 is 6

LCM of denominators i.e. for 490,419 is 205310.

Thus, GCF of Fractions is 6/205310.Finally, GCF of Fractions for 294/490, 402/419 is 6/205310.