How to Find GCF of 120/159, 7340/437?

GCF of 120/159, 7340/437

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 120/159, 7340/437 i.e 20/69483 easily. The following is the detailed procedure to determine the greatest common factor of fractions 120/159, 7340/437.

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 120/159,7340/437?

Given fractions are 120/159,7340/437

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 120/159,7340/437, numerators are 120,7340

Denominators are 159,437

The GCF of 120,7340 is 20 .

LCM of 159,437 is 69483.

The greatest common factor of 120/159,7340/437 = [GCF of 120,7340]/[LCM of 159,437]= 20/69483

Therefore, the GCF of 120/159,7340/437 is 20/69483.

Greatest Common Factor of 120,7340

To find the highest common factor of 120,7340, 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 7340 are 1, 2, 4, 5, 10, 20, 367, 734, 1468, 1835, 3670, 7340

The HCF of 120,7340 is 20.

Lets's calculate GCF of 120,7340

Greatest Common Factor (GCF) of 120,7340 By Common Division

2	120, 7340
2	60, 3670
5	30, 1835
	6, 367

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

Greatest Common Factor of 120,7340 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 7340

1,2,4,5,10,20,367,734,1468,1835,3670,7340

Greatest Common Factor

We found the factors 120,7340 . The biggest common factor number is the GCF number.
So the greatest common factor 120,7340 is 20.

Lets's calculate LCM of 159,437

Lowest Common Multiple of 159,437 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 69483

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/69483

Therefore, the GCF of Fractions 120/159,7340/437 is 20/69483

Least Common Multiple of 159,437 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 159,437 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(159,437) = 1

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

GCF(159,437) x common factors =1 x 1 = 1

LCM(159,437) = ( 159 × 437 ) / 1

LCM(159,437) = 69483 / 1

LCM(159,437) = 69483

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FAQs on GCF of Fractions of 120/159, 7340/437

1. What is the HCF of 120,7340?

The HCF of 120,7340 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 120/159, 7340/437?

Answer: GCF of Numerators as per given numbers 120/159, 7340/437 is

GCF of Numerators i.e. for 120,7340 is 20

LCM of denominators i.e. for 159,437 is 69483.

Thus, GCF of Fractions is 20/69483.Finally, GCF of Fractions for 120/159, 7340/437 is 20/69483.