How to Find GCF of 164/978, 210/682?

GCF of 164/978, 210/682

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 164/978, 210/682 i.e 2/333498 easily. The following is the detailed procedure to determine the greatest common factor of fractions 164/978, 210/682.

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 164/978,210/682?

Given fractions are 164/978,210/682

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 164/978,210/682, numerators are 164,210

Denominators are 978,682

The GCF of 164,210 is 2 .

LCM of 978,682 is 333498.

The greatest common factor of 164/978,210/682 = [GCF of 164,210]/[LCM of 978,682]= 2/333498

Therefore, the GCF of 164/978,210/682 is 2/333498.

Greatest Common Factor of 164,210

To find the highest common factor of 164,210, we have to find the factors of both numbers and list the highest common factor.

The factors of 164 are 1, 2, 4, 41, 82, 164

The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

The HCF of 164,210 is 2.

Lets's calculate GCF of 164,210

Greatest Common Factor (GCF) of 164,210 By Common Division

2	164, 210
	82, 105

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 164,210 By Matching Biggest Common Factor Method

Now, list down the factors of 164

1,2,4,41,82,164

Now, list down the factors of 210

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Greatest Common Factor

We found the factors 164,210 . The biggest common factor number is the GCF number.
So the greatest common factor 164,210 is 2.

Lets's calculate LCM of 978,682

Lowest Common Multiple of 978,682 using Common Division

2	978, 682
	489, 341

∴ So the LCM of the given numbers is 2 x 489 x 341 = 333498

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/333498

Therefore, the GCF of Fractions 164/978,210/682 is 2/333498

Least Common Multiple of 978,682 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 978,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(978,682) = 2

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

GCF(978,682) x common factors =2 x 1 = 2

LCM(978,682) = ( 978 × 682 ) / 2

LCM(978,682) = 666996 / 2

LCM(978,682) = 333498

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 164/978, 210/682

1. What is the HCF of 164,210?

The HCF of 164,210 is 2

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 164/978, 210/682?

Answer: GCF of Numerators as per given numbers 164/978, 210/682 is

GCF of Numerators i.e. for 164,210 is 2

LCM of denominators i.e. for 978,682 is 333498.

Thus, GCF of Fractions is 2/333498.Finally, GCF of Fractions for 164/978, 210/682 is 2/333498.