How to Find GCF of 570/780, 360/214?

GCF of 570/780, 360/214

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 570/780, 360/214 i.e 30/83460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 570/780, 360/214.

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 570/780,360/214?

Given fractions are 570/780,360/214

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 570/780,360/214, numerators are 570,360

Denominators are 780,214

The GCF of 570,360 is 30 .

LCM of 780,214 is 83460.

The greatest common factor of 570/780,360/214 = [GCF of 570,360]/[LCM of 780,214]= 30/83460

Therefore, the GCF of 570/780,360/214 is 30/83460.

Greatest Common Factor of 570,360

To find the highest common factor of 570,360, we have to find the factors of both numbers and list the highest common factor.

The factors of 570 are 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

The HCF of 570,360 is 30.

Lets's calculate GCF of 570,360

Greatest Common Factor (GCF) of 570,360 By Common Division

2	570, 360
3	285, 180
5	95, 60
	19, 12

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

Greatest Common Factor of 570,360 By Matching Biggest Common Factor Method

Now, list down the factors of 570

1,2,3,5,6,10,15,19,30,38,57,95,114,190,285,570

Now, list down the factors of 360

1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360

Greatest Common Factor

We found the factors 570,360 . The biggest common factor number is the GCF number.
So the greatest common factor 570,360 is 30.

Lets's calculate LCM of 780,214

Lowest Common Multiple of 780,214 using Common Division

2	780, 214
	390, 107

∴ So the LCM of the given numbers is 2 x 390 x 107 = 83460

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/83460

Therefore, the GCF of Fractions 570/780,360/214 is 30/83460

Least Common Multiple of 780,214 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 780,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(780,214) = 2

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

GCF(780,214) x common factors =2 x 1 = 2

LCM(780,214) = ( 780 × 214 ) / 2

LCM(780,214) = 166920 / 2

LCM(780,214) = 83460

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FAQs on GCF of Fractions of 570/780, 360/214

1. What is the HCF of 570,360?

The HCF of 570,360 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 570/780, 360/214?

Answer: GCF of Numerators as per given numbers 570/780, 360/214 is

GCF of Numerators i.e. for 570,360 is 30

LCM of denominators i.e. for 780,214 is 83460.

Thus, GCF of Fractions is 30/83460.Finally, GCF of Fractions for 570/780, 360/214 is 30/83460.