How to Find GCF of 313/16, 492/62, 289/70?

GCF of 313/16, 492/62, 289/70

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 313/16, 492/62, 289/70 i.e 1/17360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 313/16, 492/62, 289/70.

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 313/16,492/62,289/70?

Given fractions are 313/16,492/62,289/70

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 313/16,492/62,289/70, numerators are 313,492,289

Denominators are 16,62,70

The GCF of 313,492,289 is 1 .

LCM of 16,62,70 is 17360.

The greatest common factor of 313/16,492/62,289/70 = [GCF of 313,492,289]/[LCM of 16,62,70]= 1/17360

Therefore, the GCF of 313/16,492/62,289/70 is 1/17360.

Greatest Common Factor of 313,492,289

To find the highest common factor of 313,492,289, we have to find the factors of both numbers and list the highest common factor.

The factors of 313 are 1, 313

The factors of 492 are 1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 492

The factors of 289 are 1, 17, 289

The HCF of 313,492,289 is 1.

Lets's calculate GCF of 313,492,289

Greatest Common Factor (GCF) of 313,492,289 By Common Division

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

Greatest Common Factor of 313,492,289 By Matching Biggest Common Factor Method

Now, list down the factors of 313

1,313

Now, list down the factors of 492

1,2,3,4,6,12,41,82,123,164,246,492

Now, list down the factors of 289

1,17,289

Greatest Common Factor

We found the factors 313,492,289 . The biggest common factor number is the GCF number.
So the greatest common factor 313,492,289 is 1.

Lets's calculate LCM of 16,62,70

Lowest Common Multiple of 16,62,70 using Common Division

2	16, 62, 70
	8, 31, 35

∴ So the LCM of the given numbers is 2 x 8 x 31 x 35 = 17360

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17360

Therefore, the GCF of Fractions 313/16,492/62,289/70 is 1/17360

Least Common Multiple of 16,62,70 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 16,62,70 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,62,70) = 2

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

GCF(16,62,70) x common factors =2 x 2 = 4

LCM(16,62,70) = ( 16 × 62 × 70 ) / 4

LCM(16,62,70) = 69440 / 4

LCM(16,62,70) = 17360

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 313/16, 492/62, 289/70

1. What is the HCF of 313,492,289?

The HCF of 313,492,289 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 313/16, 492/62, 289/70?

Answer: GCF of Numerators as per given numbers 313/16, 492/62, 289/70 is

GCF of Numerators i.e. for 313,492,289 is 1

LCM of denominators i.e. for 16,62,70 is 17360.

Thus, GCF of Fractions is 1/17360.Finally, GCF of Fractions for 313/16, 492/62, 289/70 is 1/17360.