How to Find GCF of 210/12, 870/8292?

GCF of 210/12, 870/8292

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 210/12, 870/8292 i.e 30/8292 easily. The following is the detailed procedure to determine the greatest common factor of fractions 210/12, 870/8292.

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 210/12,870/8292?

Given fractions are 210/12,870/8292

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 210/12,870/8292, numerators are 210,870

Denominators are 12,8292

The GCF of 210,870 is 30 .

LCM of 12,8292 is 8292.

The greatest common factor of 210/12,870/8292 = [GCF of 210,870]/[LCM of 12,8292]= 30/8292

Therefore, the GCF of 210/12,870/8292 is 30/8292.

Greatest Common Factor of 210,870

To find the highest common factor of 210,870, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

The HCF of 210,870 is 30.

Lets's calculate GCF of 210,870

Greatest Common Factor (GCF) of 210,870 By Common Division

2	210, 870
3	105, 435
5	35, 145
	7, 29

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

Greatest Common Factor of 210,870 By Matching Biggest Common Factor Method

Now, list down the factors of 210

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

Now, list down the factors of 870

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Greatest Common Factor

We found the factors 210,870 . The biggest common factor number is the GCF number.
So the greatest common factor 210,870 is 30.

Lets's calculate LCM of 12,8292

Lowest Common Multiple of 12,8292 using Common Division

2	12, 8292
2	6, 4146
3	3, 2073
	1, 691

∴ So the LCM of the given numbers is 2 x 2 x 3 x 1 x 691 = 8292

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/8292

Therefore, the GCF of Fractions 210/12,870/8292 is 30/8292

Least Common Multiple of 12,8292 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 12,8292 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,8292) = 12

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

GCF(12,8292) x common factors =12 x 1 = 12

LCM(12,8292) = ( 12 × 8292 ) / 12

LCM(12,8292) = 99504 / 12

LCM(12,8292) = 8292

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FAQs on GCF of Fractions of 210/12, 870/8292

1. What is the HCF of 210,870?

The HCF of 210,870 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 210/12, 870/8292?

Answer: GCF of Numerators as per given numbers 210/12, 870/8292 is

GCF of Numerators i.e. for 210,870 is 30

LCM of denominators i.e. for 12,8292 is 8292.

Thus, GCF of Fractions is 30/8292.Finally, GCF of Fractions for 210/12, 870/8292 is 30/8292.