How to Find GCF of 630/603, 610/825?

GCF of 630/603, 610/825

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 630/603, 610/825 i.e 10/165825 easily. The following is the detailed procedure to determine the greatest common factor of fractions 630/603, 610/825.

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 630/603,610/825?

Given fractions are 630/603,610/825

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 630/603,610/825, numerators are 630,610

Denominators are 603,825

The GCF of 630,610 is 10 .

LCM of 603,825 is 165825.

The greatest common factor of 630/603,610/825 = [GCF of 630,610]/[LCM of 603,825]= 10/165825

Therefore, the GCF of 630/603,610/825 is 10/165825.

Greatest Common Factor of 630,610

To find the highest common factor of 630,610, we have to find the factors of both numbers and list the highest common factor.

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 factors of 610 are 1, 2, 5, 10, 61, 122, 305, 610

The HCF of 630,610 is 10.

Lets's calculate GCF of 630,610

Greatest Common Factor (GCF) of 630,610 By Common Division

2	630, 610
5	315, 305
	63, 61

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

Greatest Common Factor of 630,610 By Matching Biggest Common Factor Method

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

Now, list down the factors of 610

1,2,5,10,61,122,305,610

Greatest Common Factor

We found the factors 630,610 . The biggest common factor number is the GCF number.
So the greatest common factor 630,610 is 10.

Lets's calculate LCM of 603,825

Lowest Common Multiple of 603,825 using Common Division

3	603, 825
	201, 275

∴ So the LCM of the given numbers is 3 x 201 x 275 = 165825

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/165825

Therefore, the GCF of Fractions 630/603,610/825 is 10/165825

Least Common Multiple of 603,825 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 603,825 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(603,825) = 3

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

GCF(603,825) x common factors =3 x 1 = 3

LCM(603,825) = ( 603 × 825 ) / 3

LCM(603,825) = 497475 / 3

LCM(603,825) = 165825

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FAQs on GCF of Fractions of 630/603, 610/825

1. What is the HCF of 630,610?

The HCF of 630,610 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 630/603, 610/825?

Answer: GCF of Numerators as per given numbers 630/603, 610/825 is

GCF of Numerators i.e. for 630,610 is 10

LCM of denominators i.e. for 603,825 is 165825.

Thus, GCF of Fractions is 10/165825.Finally, GCF of Fractions for 630/603, 610/825 is 10/165825.