How to Find GCF of 630/31, 120/7863?

GCF of 630/31, 120/7863

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 630/31, 120/7863 i.e 30/243753 easily. The following is the detailed procedure to determine the greatest common factor of fractions 630/31, 120/7863.

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 630/31,120/7863?

Given fractions are 630/31,120/7863

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 630/31,120/7863, numerators are 630,120

Denominators are 31,7863

The GCF of 630,120 is 30 .

LCM of 31,7863 is 243753.

The greatest common factor of 630/31,120/7863 = [GCF of 630,120]/[LCM of 31,7863]= 30/243753

Therefore, the GCF of 630/31,120/7863 is 30/243753.

Greatest Common Factor of 630,120

To find the highest common factor of 630,120, 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 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The HCF of 630,120 is 30.

Lets's calculate GCF of 630,120

Greatest Common Factor (GCF) of 630,120 By Common Division

2	630, 120
3	315, 60
5	105, 20
	21, 4

∴ So the GCF of the given numbers is 2 x 3 x 5 = 30

Greatest Common Factor of 630,120 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 120

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Greatest Common Factor

We found the factors 630,120 . The biggest common factor number is the GCF number.
So the greatest common factor 630,120 is 30.

Lets's calculate LCM of 31,7863

Lowest Common Multiple of 31,7863 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 243753

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/243753

Therefore, the GCF of Fractions 630/31,120/7863 is 30/243753

Least Common Multiple of 31,7863 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 31,7863 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,7863) = 1

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

GCF(31,7863) x common factors =1 x 1 = 1

LCM(31,7863) = ( 31 × 7863 ) / 1

LCM(31,7863) = 243753 / 1

LCM(31,7863) = 243753

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 630/31, 120/7863

1. What is the HCF of 630,120?

The HCF of 630,120 is 30

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 630/31, 120/7863?

Answer: GCF of Numerators as per given numbers 630/31, 120/7863 is

GCF of Numerators i.e. for 630,120 is 30

LCM of denominators i.e. for 31,7863 is 243753.

Thus, GCF of Fractions is 30/243753.Finally, GCF of Fractions for 630/31, 120/7863 is 30/243753.