How to Find GCF of 493/522, 630/590?

GCF of 493/522, 630/590

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 493/522, 630/590 i.e 1/153990 easily. The following is the detailed procedure to determine the greatest common factor of fractions 493/522, 630/590.

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 493/522,630/590?

Given fractions are 493/522,630/590

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 493/522,630/590, numerators are 493,630

Denominators are 522,590

The GCF of 493,630 is 1 .

LCM of 522,590 is 153990.

The greatest common factor of 493/522,630/590 = [GCF of 493,630]/[LCM of 522,590]= 1/153990

Therefore, the GCF of 493/522,630/590 is 1/153990.

Greatest Common Factor of 493,630

To find the highest common factor of 493,630, we have to find the factors of both numbers and list the highest common factor.

The factors of 493 are 1, 17, 29, 493

The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630

The HCF of 493,630 is 1.

Lets's calculate GCF of 493,630

Greatest Common Factor (GCF) of 493,630 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 493,630 By Matching Biggest Common Factor Method

Now, list down the factors of 493

1,17,29,493

Now, list down the factors of 630

1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630

Greatest Common Factor

We found the factors 493,630 . The biggest common factor number is the GCF number.
So the greatest common factor 493,630 is 1.

Lets's calculate LCM of 522,590

Lowest Common Multiple of 522,590 using Common Division

2	522, 590
	261, 295

∴ So the LCM of the given numbers is 2 x 261 x 295 = 153990

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/153990

Therefore, the GCF of Fractions 493/522,630/590 is 1/153990

Least Common Multiple of 522,590 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 522,590 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(522,590) = 2

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

GCF(522,590) x common factors =2 x 1 = 2

LCM(522,590) = ( 522 × 590 ) / 2

LCM(522,590) = 307980 / 2

LCM(522,590) = 153990

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FAQs on GCF of Fractions of 493/522, 630/590

1. What is the HCF of 493,630?

The HCF of 493,630 is 1

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 493/522, 630/590?

Answer: GCF of Numerators as per given numbers 493/522, 630/590 is

GCF of Numerators i.e. for 493,630 is 1

LCM of denominators i.e. for 522,590 is 153990.

Thus, GCF of Fractions is 1/153990.Finally, GCF of Fractions for 493/522, 630/590 is 1/153990.