How to Find GCF of 469/72, 870/514?

GCF of 469/72, 870/514

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 469/72, 870/514 i.e 1/18504 easily. The following is the detailed procedure to determine the greatest common factor of fractions 469/72, 870/514.

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 469/72,870/514?

Given fractions are 469/72,870/514

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 469/72,870/514, numerators are 469,870

Denominators are 72,514

The GCF of 469,870 is 1 .

LCM of 72,514 is 18504.

The greatest common factor of 469/72,870/514 = [GCF of 469,870]/[LCM of 72,514]= 1/18504

Therefore, the GCF of 469/72,870/514 is 1/18504.

Greatest Common Factor of 469,870

To find the highest common factor of 469,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 469 are 1, 7, 67, 469

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

The HCF of 469,870 is 1.

Lets's calculate GCF of 469,870

Greatest Common Factor (GCF) of 469,870 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 469,870 By Matching Biggest Common Factor Method

Now, list down the factors of 469

1,7,67,469

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 469,870 . The biggest common factor number is the GCF number.
So the greatest common factor 469,870 is 1.

Lets's calculate LCM of 72,514

Lowest Common Multiple of 72,514 using Common Division

2	72, 514
	36, 257

∴ So the LCM of the given numbers is 2 x 36 x 257 = 18504

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18504

Therefore, the GCF of Fractions 469/72,870/514 is 1/18504

Least Common Multiple of 72,514 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 72,514 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(72,514) = 2

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

GCF(72,514) x common factors =2 x 1 = 2

LCM(72,514) = ( 72 × 514 ) / 2

LCM(72,514) = 37008 / 2

LCM(72,514) = 18504

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FAQs on GCF of Fractions of 469/72, 870/514

1. What is the HCF of 469,870?

The HCF of 469,870 is 1

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 469/72, 870/514?

Answer: GCF of Numerators as per given numbers 469/72, 870/514 is

GCF of Numerators i.e. for 469,870 is 1

LCM of denominators i.e. for 72,514 is 18504.

Thus, GCF of Fractions is 1/18504.Finally, GCF of Fractions for 469/72, 870/514 is 1/18504.