How to Find GCF of 120/436, 380/468?

GCF of 120/436, 380/468

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 120/436, 380/468 i.e 20/51012 easily. The following is the detailed procedure to determine the greatest common factor of fractions 120/436, 380/468.

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 120/436,380/468?

Given fractions are 120/436,380/468

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 120/436,380/468, numerators are 120,380

Denominators are 436,468

The GCF of 120,380 is 20 .

LCM of 436,468 is 51012.

The greatest common factor of 120/436,380/468 = [GCF of 120,380]/[LCM of 436,468]= 20/51012

Therefore, the GCF of 120/436,380/468 is 20/51012.

Greatest Common Factor of 120,380

To find the highest common factor of 120,380, we have to find the factors of both numbers and list the highest common factor.

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380

The HCF of 120,380 is 20.

Lets's calculate GCF of 120,380

Greatest Common Factor (GCF) of 120,380 By Common Division

2	120, 380
2	60, 190
5	30, 95
	6, 19

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

Greatest Common Factor of 120,380 By Matching Biggest Common Factor Method

Now, list down the factors of 120

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Now, list down the factors of 380

1,2,4,5,10,19,20,38,76,95,190,380

Greatest Common Factor

We found the factors 120,380 . The biggest common factor number is the GCF number.
So the greatest common factor 120,380 is 20.

Lets's calculate LCM of 436,468

Lowest Common Multiple of 436,468 using Common Division

2	436, 468
2	218, 234
	109, 117

∴ So the LCM of the given numbers is 2 x 2 x 109 x 117 = 51012

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/51012

Therefore, the GCF of Fractions 120/436,380/468 is 20/51012

Least Common Multiple of 436,468 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 436,468 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(436,468) = 4

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

GCF(436,468) x common factors =4 x 1 = 4

LCM(436,468) = ( 436 × 468 ) / 4

LCM(436,468) = 204048 / 4

LCM(436,468) = 51012

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FAQs on GCF of Fractions of 120/436, 380/468

1. What is the HCF of 120,380?

The HCF of 120,380 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 120/436, 380/468?

Answer: GCF of Numerators as per given numbers 120/436, 380/468 is

GCF of Numerators i.e. for 120,380 is 20

LCM of denominators i.e. for 436,468 is 51012.

Thus, GCF of Fractions is 20/51012.Finally, GCF of Fractions for 120/436, 380/468 is 20/51012.