How to Find GCF of 690/24, 870/1356?

GCF of 690/24, 870/1356

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 690/24, 870/1356 i.e 30/2712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 690/24, 870/1356.

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 690/24,870/1356?

Given fractions are 690/24,870/1356

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 690/24,870/1356, numerators are 690,870

Denominators are 24,1356

The GCF of 690,870 is 30 .

LCM of 24,1356 is 2712.

The greatest common factor of 690/24,870/1356 = [GCF of 690,870]/[LCM of 24,1356]= 30/2712

Therefore, the GCF of 690/24,870/1356 is 30/2712.

Greatest Common Factor of 690,870

To find the highest common factor of 690,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690

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

The HCF of 690,870 is 30.

Lets's calculate GCF of 690,870

Greatest Common Factor (GCF) of 690,870 By Common Division

2	690, 870
3	345, 435
5	115, 145
	23, 29

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

Greatest Common Factor of 690,870 By Matching Biggest Common Factor Method

Now, list down the factors of 690

1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690

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 690,870 . The biggest common factor number is the GCF number.
So the greatest common factor 690,870 is 30.

Lets's calculate LCM of 24,1356

Lowest Common Multiple of 24,1356 using Common Division

2	24, 1356
2	12, 678
3	6, 339
	2, 113

∴ So the LCM of the given numbers is 2 x 2 x 3 x 2 x 113 = 2712

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/2712

Therefore, the GCF of Fractions 690/24,870/1356 is 30/2712

Least Common Multiple of 24,1356 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 24,1356 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(24,1356) = 12

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

GCF(24,1356) x common factors =12 x 1 = 12

LCM(24,1356) = ( 24 × 1356 ) / 12

LCM(24,1356) = 32544 / 12

LCM(24,1356) = 2712

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 690/24, 870/1356

1. What is the HCF of 690,870?

The HCF of 690,870 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 690/24, 870/1356?

Answer: GCF of Numerators as per given numbers 690/24, 870/1356 is

GCF of Numerators i.e. for 690,870 is 30

LCM of denominators i.e. for 24,1356 is 2712.

Thus, GCF of Fractions is 30/2712.Finally, GCF of Fractions for 690/24, 870/1356 is 30/2712.