How to Find GCF of 300/169, 580/632?

GCF of 300/169, 580/632

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 300/169, 580/632 i.e 20/106808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 300/169, 580/632.

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 300/169,580/632?

Given fractions are 300/169,580/632

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 300/169,580/632, numerators are 300,580

Denominators are 169,632

The GCF of 300,580 is 20 .

LCM of 169,632 is 106808.

The greatest common factor of 300/169,580/632 = [GCF of 300,580]/[LCM of 169,632]= 20/106808

Therefore, the GCF of 300/169,580/632 is 20/106808.

Greatest Common Factor of 300,580

To find the highest common factor of 300,580, we have to find the factors of both numbers and list the highest common factor.

The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580

The HCF of 300,580 is 20.

Lets's calculate GCF of 300,580

Greatest Common Factor (GCF) of 300,580 By Common Division

2	300, 580
2	150, 290
5	75, 145
	15, 29

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 300,580 By Matching Biggest Common Factor Method

Now, list down the factors of 300

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Now, list down the factors of 580

1,2,4,5,10,20,29,58,116,145,290,580

Greatest Common Factor

We found the factors 300,580 . The biggest common factor number is the GCF number.
So the greatest common factor 300,580 is 20.

Lets's calculate LCM of 169,632

Lowest Common Multiple of 169,632 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 106808

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/106808

Therefore, the GCF of Fractions 300/169,580/632 is 20/106808

Least Common Multiple of 169,632 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 169,632 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(169,632) = 1

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

GCF(169,632) x common factors =1 x 1 = 1

LCM(169,632) = ( 169 × 632 ) / 1

LCM(169,632) = 106808 / 1

LCM(169,632) = 106808

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FAQs on GCF of Fractions of 300/169, 580/632

1. What is the HCF of 300,580?

The HCF of 300,580 is 20

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 300/169, 580/632?

Answer: GCF of Numerators as per given numbers 300/169, 580/632 is

GCF of Numerators i.e. for 300,580 is 20

LCM of denominators i.e. for 169,632 is 106808.

Thus, GCF of Fractions is 20/106808.Finally, GCF of Fractions for 300/169, 580/632 is 20/106808.