How to Find GCF of 400/563, 490/834?

GCF of 400/563, 490/834

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 400/563, 490/834 i.e 10/469542 easily. The following is the detailed procedure to determine the greatest common factor of fractions 400/563, 490/834.

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 400/563,490/834?

Given fractions are 400/563,490/834

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 400/563,490/834, numerators are 400,490

Denominators are 563,834

The GCF of 400,490 is 10 .

LCM of 563,834 is 469542.

The greatest common factor of 400/563,490/834 = [GCF of 400,490]/[LCM of 563,834]= 10/469542

Therefore, the GCF of 400/563,490/834 is 10/469542.

Greatest Common Factor of 400,490

To find the highest common factor of 400,490, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490

The HCF of 400,490 is 10.

Lets's calculate GCF of 400,490

Greatest Common Factor (GCF) of 400,490 By Common Division

2	400, 490
5	200, 245
	40, 49

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 400,490 By Matching Biggest Common Factor Method

Now, list down the factors of 400

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

Now, list down the factors of 490

1,2,5,7,10,14,35,49,70,98,245,490

Greatest Common Factor

We found the factors 400,490 . The biggest common factor number is the GCF number.
So the greatest common factor 400,490 is 10.

Lets's calculate LCM of 563,834

Lowest Common Multiple of 563,834 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 469542

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/469542

Therefore, the GCF of Fractions 400/563,490/834 is 10/469542

Least Common Multiple of 563,834 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 563,834 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(563,834) = 1

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

GCF(563,834) x common factors =1 x 1 = 1

LCM(563,834) = ( 563 × 834 ) / 1

LCM(563,834) = 469542 / 1

LCM(563,834) = 469542

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FAQs on GCF of Fractions of 400/563, 490/834

1. What is the HCF of 400,490?

The HCF of 400,490 is 10

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 400/563, 490/834?

Answer: GCF of Numerators as per given numbers 400/563, 490/834 is

GCF of Numerators i.e. for 400,490 is 10

LCM of denominators i.e. for 563,834 is 469542.

Thus, GCF of Fractions is 10/469542.Finally, GCF of Fractions for 400/563, 490/834 is 10/469542.