How to Find GCF of 288/22, 210/505?

GCF of 288/22, 210/505

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 288/22, 210/505 i.e 6/11110 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/22, 210/505.

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 288/22,210/505?

Given fractions are 288/22,210/505

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 288/22,210/505, numerators are 288,210

Denominators are 22,505

The GCF of 288,210 is 6 .

LCM of 22,505 is 11110.

The greatest common factor of 288/22,210/505 = [GCF of 288,210]/[LCM of 22,505]= 6/11110

Therefore, the GCF of 288/22,210/505 is 6/11110.

Greatest Common Factor of 288,210

To find the highest common factor of 288,210, we have to find the factors of both numbers and list the highest common factor.

The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

The HCF of 288,210 is 6.

Lets's calculate GCF of 288,210

Greatest Common Factor (GCF) of 288,210 By Common Division

2	288, 210
3	144, 105
	48, 35

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 288,210 By Matching Biggest Common Factor Method

Now, list down the factors of 288

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288

Now, list down the factors of 210

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Greatest Common Factor

We found the factors 288,210 . The biggest common factor number is the GCF number.
So the greatest common factor 288,210 is 6.

Lets's calculate LCM of 22,505

Lowest Common Multiple of 22,505 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 11110

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/11110

Therefore, the GCF of Fractions 288/22,210/505 is 6/11110

Least Common Multiple of 22,505 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 22,505 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(22,505) = 1

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

GCF(22,505) x common factors =1 x 1 = 1

LCM(22,505) = ( 22 × 505 ) / 1

LCM(22,505) = 11110 / 1

LCM(22,505) = 11110

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 288/22, 210/505

1. What is the HCF of 288,210?

The HCF of 288,210 is 6

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 288/22, 210/505?

Answer: GCF of Numerators as per given numbers 288/22, 210/505 is

GCF of Numerators i.e. for 288,210 is 6

LCM of denominators i.e. for 22,505 is 11110.

Thus, GCF of Fractions is 6/11110.Finally, GCF of Fractions for 288/22, 210/505 is 6/11110.