How to Find GCF of 120/14, 540/206?

GCF of 120/14, 540/206

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 120/14, 540/206 i.e 60/1442 easily. The following is the detailed procedure to determine the greatest common factor of fractions 120/14, 540/206.

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 120/14,540/206?

Given fractions are 120/14,540/206

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 120/14,540/206, numerators are 120,540

Denominators are 14,206

The GCF of 120,540 is 60 .

LCM of 14,206 is 1442.

The greatest common factor of 120/14,540/206 = [GCF of 120,540]/[LCM of 14,206]= 60/1442

Therefore, the GCF of 120/14,540/206 is 60/1442.

Greatest Common Factor of 120,540

To find the highest common factor of 120,540, 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 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

The HCF of 120,540 is 60.

Lets's calculate GCF of 120,540

Greatest Common Factor (GCF) of 120,540 By Common Division

2	120, 540
2	60, 270
3	30, 135
5	10, 45
	2, 9

∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60

Greatest Common Factor of 120,540 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 540

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Greatest Common Factor

We found the factors 120,540 . The biggest common factor number is the GCF number.
So the greatest common factor 120,540 is 60.

Lets's calculate LCM of 14,206

Lowest Common Multiple of 14,206 using Common Division

2	14, 206
	7, 103

∴ So the LCM of the given numbers is 2 x 7 x 103 = 1442

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/1442

Therefore, the GCF of Fractions 120/14,540/206 is 60/1442

Least Common Multiple of 14,206 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 14,206 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,206) = 2

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

GCF(14,206) x common factors =2 x 1 = 2

LCM(14,206) = ( 14 × 206 ) / 2

LCM(14,206) = 2884 / 2

LCM(14,206) = 1442

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 120/14, 540/206

1. What is the HCF of 120,540?

The HCF of 120,540 is 60

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 120/14, 540/206?

Answer: GCF of Numerators as per given numbers 120/14, 540/206 is

GCF of Numerators i.e. for 120,540 is 60

LCM of denominators i.e. for 14,206 is 1442.

Thus, GCF of Fractions is 60/1442.Finally, GCF of Fractions for 120/14, 540/206 is 60/1442.