How to Find GCF of 284/164, 870/544?

GCF of 284/164, 870/544

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 284/164, 870/544 i.e 2/22304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 284/164, 870/544.

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 284/164,870/544?

Given fractions are 284/164,870/544

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 284/164,870/544, numerators are 284,870

Denominators are 164,544

The GCF of 284,870 is 2 .

LCM of 164,544 is 22304.

The greatest common factor of 284/164,870/544 = [GCF of 284,870]/[LCM of 164,544]= 2/22304

Therefore, the GCF of 284/164,870/544 is 2/22304.

Greatest Common Factor of 284,870

To find the highest common factor of 284,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 284 are 1, 2, 4, 71, 142, 284

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

The HCF of 284,870 is 2.

Lets's calculate GCF of 284,870

Greatest Common Factor (GCF) of 284,870 By Common Division

2	284, 870
	142, 435

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 284,870 By Matching Biggest Common Factor Method

Now, list down the factors of 284

1,2,4,71,142,284

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 284,870 . The biggest common factor number is the GCF number.
So the greatest common factor 284,870 is 2.

Lets's calculate LCM of 164,544

Lowest Common Multiple of 164,544 using Common Division

2	164, 544
2	82, 272
	41, 136

∴ So the LCM of the given numbers is 2 x 2 x 41 x 136 = 22304

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/22304

Therefore, the GCF of Fractions 284/164,870/544 is 2/22304

Least Common Multiple of 164,544 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 164,544 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(164,544) = 4

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

GCF(164,544) x common factors =4 x 1 = 4

LCM(164,544) = ( 164 × 544 ) / 4

LCM(164,544) = 89216 / 4

LCM(164,544) = 22304

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FAQs on GCF of Fractions of 284/164, 870/544

1. What is the HCF of 284,870?

The HCF of 284,870 is 2

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 284/164, 870/544?

Answer: GCF of Numerators as per given numbers 284/164, 870/544 is

GCF of Numerators i.e. for 284,870 is 2

LCM of denominators i.e. for 164,544 is 22304.

Thus, GCF of Fractions is 2/22304.Finally, GCF of Fractions for 284/164, 870/544 is 2/22304.