How to Find GCF of 468/82, 630/253?

GCF of 468/82, 630/253

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 468/82, 630/253 i.e 18/20746 easily. The following is the detailed procedure to determine the greatest common factor of fractions 468/82, 630/253.

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 468/82,630/253?

Given fractions are 468/82,630/253

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 468/82,630/253, numerators are 468,630

Denominators are 82,253

The GCF of 468,630 is 18 .

LCM of 82,253 is 20746.

The greatest common factor of 468/82,630/253 = [GCF of 468,630]/[LCM of 82,253]= 18/20746

Therefore, the GCF of 468/82,630/253 is 18/20746.

Greatest Common Factor of 468,630

To find the highest common factor of 468,630, we have to find the factors of both numbers and list the highest common factor.

The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468

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 468,630 is 18.

Lets's calculate GCF of 468,630

Greatest Common Factor (GCF) of 468,630 By Common Division

2	468, 630
3	234, 315
3	78, 105
	26, 35

∴ So the GCF of the given numbers is 2 x 3 x 3 = 18

Greatest Common Factor of 468,630 By Matching Biggest Common Factor Method

Now, list down the factors of 468

1,2,3,4,6,9,12,13,18,26,36,39,52,78,117,156,234,468

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 468,630 . The biggest common factor number is the GCF number.
So the greatest common factor 468,630 is 18.

Lets's calculate LCM of 82,253

Lowest Common Multiple of 82,253 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 20746

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/20746

Therefore, the GCF of Fractions 468/82,630/253 is 18/20746

Least Common Multiple of 82,253 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 82,253 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(82,253) = 1

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

GCF(82,253) x common factors =1 x 1 = 1

LCM(82,253) = ( 82 × 253 ) / 1

LCM(82,253) = 20746 / 1

LCM(82,253) = 20746

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 468/82, 630/253

1. What is the HCF of 468,630?

The HCF of 468,630 is 18

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 468/82, 630/253?

Answer: GCF of Numerators as per given numbers 468/82, 630/253 is

GCF of Numerators i.e. for 468,630 is 18

LCM of denominators i.e. for 82,253 is 20746.

Thus, GCF of Fractions is 18/20746.Finally, GCF of Fractions for 468/82, 630/253 is 18/20746.