How to Find GCF of 65/58, 353/20, 870/367?

GCF of 65/58, 353/20, 870/367

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 65/58, 353/20, 870/367 i.e 1/212860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/58, 353/20, 870/367.

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 65/58,353/20,870/367?

Given fractions are 65/58,353/20,870/367

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 65/58,353/20,870/367, numerators are 65,353,870

Denominators are 58,20,367

The GCF of 65,353,870 is 1 .

LCM of 58,20,367 is 212860.

The greatest common factor of 65/58,353/20,870/367 = [GCF of 65,353,870]/[LCM of 58,20,367]= 1/212860

Therefore, the GCF of 65/58,353/20,870/367 is 1/212860.

Greatest Common Factor of 65,353,870

To find the highest common factor of 65,353,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 65 are 1, 5, 13, 65

The factors of 353 are 1, 353

The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

The HCF of 65,353,870 is 1.

Lets's calculate GCF of 65,353,870

Greatest Common Factor (GCF) of 65,353,870 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 65,353,870 By Matching Biggest Common Factor Method

Now, list down the factors of 65

1,5,13,65

Now, list down the factors of 353

1,353

Now, list down the factors of 870

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Greatest Common Factor

We found the factors 65,353,870 . The biggest common factor number is the GCF number.
So the greatest common factor 65,353,870 is 1.

Lets's calculate LCM of 58,20,367

Lowest Common Multiple of 58,20,367 using Common Division

2	58, 20, 367
	29, 10, 367

∴ So the LCM of the given numbers is 2 x 29 x 10 x 367 = 212860

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/212860

Therefore, the GCF of Fractions 65/58,353/20,870/367 is 1/212860

Least Common Multiple of 58,20,367 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 58,20,367 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(58,20,367) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(58,20,367) x common factors =1 x 2 = 2

LCM(58,20,367) = ( 58 × 20 × 367 ) / 2

LCM(58,20,367) = 425720 / 2

LCM(58,20,367) = 212860

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 65/58, 353/20, 870/367

1. What is the HCF of 65,353,870?

The HCF of 65,353,870 is 1

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 65/58, 353/20, 870/367?

Answer: GCF of Numerators as per given numbers 65/58, 353/20, 870/367 is

GCF of Numerators i.e. for 65,353,870 is 1

LCM of denominators i.e. for 58,20,367 is 212860.

Thus, GCF of Fractions is 1/212860.Finally, GCF of Fractions for 65/58, 353/20, 870/367 is 1/212860.