How to Find GCF of 240/83, 120/581?

GCF of 240/83, 120/581

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 240/83, 120/581 i.e 120/581 easily. The following is the detailed procedure to determine the greatest common factor of fractions 240/83, 120/581.

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 240/83,120/581?

Given fractions are 240/83,120/581

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 240/83,120/581, numerators are 240,120

Denominators are 83,581

The GCF of 240,120 is 120 .

LCM of 83,581 is 581.

The greatest common factor of 240/83,120/581 = [GCF of 240,120]/[LCM of 83,581]= 120/581

Therefore, the GCF of 240/83,120/581 is 120/581.

Greatest Common Factor of 240,120

To find the highest common factor of 240,120, we have to find the factors of both numbers and list the highest common factor.

The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

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

The HCF of 240,120 is 120.

Lets's calculate GCF of 240,120

Greatest Common Factor (GCF) of 240,120 By Common Division

2	240, 120
2	120, 60
2	30, 60
3	15, 30
5	5, 10
	1, 2

∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 5 = 120

Greatest Common Factor of 240,120 By Matching Biggest Common Factor Method

Now, list down the factors of 240

1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240

Now, list down the factors of 120

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

Greatest Common Factor

We found the factors 240,120 . The biggest common factor number is the GCF number.
So the greatest common factor 240,120 is 120.

Lets's calculate LCM of 83,581

Lowest Common Multiple of 83,581 using Common Division

83	83, 581
	1, 7

∴ So the LCM of the given numbers is 83 x 1 x 7 = 581

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 120/581

Therefore, the GCF of Fractions 240/83,120/581 is 120/581

Least Common Multiple of 83,581 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 83,581 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(83,581) = 83

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

GCF(83,581) x common factors =83 x 1 = 83

LCM(83,581) = ( 83 × 581 ) / 83

LCM(83,581) = 48223 / 83

LCM(83,581) = 581

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FAQs on GCF of Fractions of 240/83, 120/581

1. What is the HCF of 240,120?

The HCF of 240,120 is 120

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 240/83, 120/581?

Answer: GCF of Numerators as per given numbers 240/83, 120/581 is

GCF of Numerators i.e. for 240,120 is 120

LCM of denominators i.e. for 83,581 is 581.

Thus, GCF of Fractions is 120/581.Finally, GCF of Fractions for 240/83, 120/581 is 120/581.