How to Find GCF of 70/289, 10/697, 274/291?

GCF of 70/289, 10/697, 274/291

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 70/289, 10/697, 274/291 i.e 2/3448059 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/289, 10/697, 274/291.

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 70/289,10/697,274/291?

Given fractions are 70/289,10/697,274/291

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 70/289,10/697,274/291, numerators are 70,10,274

Denominators are 289,697,291

The GCF of 70,10,274 is 2 .

LCM of 289,697,291 is 3448059.

The greatest common factor of 70/289,10/697,274/291 = [GCF of 70,10,274]/[LCM of 289,697,291]= 2/3448059

Therefore, the GCF of 70/289,10/697,274/291 is 2/3448059.

Greatest Common Factor of 70,10,274

To find the highest common factor of 70,10,274, we have to find the factors of both numbers and list the highest common factor.

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70

The factors of 10 are 1, 2, 5, 10

The factors of 274 are 1, 2, 137, 274

The HCF of 70,10,274 is 2.

Lets's calculate GCF of 70,10,274

Greatest Common Factor (GCF) of 70,10,274 By Common Division

2	70, 10, 274
	35, 5, 137

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

Greatest Common Factor of 70,10,274 By Matching Biggest Common Factor Method

Now, list down the factors of 70

1,2,5,7,10,14,35,70

Now, list down the factors of 10

1,2,5,10

Now, list down the factors of 274

1,2,137,274

Greatest Common Factor

We found the factors 70,10,274 . The biggest common factor number is the GCF number.
So the greatest common factor 70,10,274 is 2.

Lets's calculate LCM of 289,697,291

Lowest Common Multiple of 289,697,291 using Common Division

17	289, 697, 291
	17, 41, 291

∴ So the LCM of the given numbers is 17 x 17 x 41 x 291 = 3448059

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3448059

Therefore, the GCF of Fractions 70/289,10/697,274/291 is 2/3448059

Least Common Multiple of 289,697,291 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 289,697,291 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,697,291) = 1

common factors(in case of two or more numbers have common factors) = 17

GCF(289,697,291) x common factors =1 x 17 = 17

LCM(289,697,291) = ( 289 × 697 × 291 ) / 17

LCM(289,697,291) = 58617003 / 17

LCM(289,697,291) = 3448059

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 70/289, 10/697, 274/291

1. What is the HCF of 70,10,274?

The HCF of 70,10,274 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 70/289, 10/697, 274/291?

Answer: GCF of Numerators as per given numbers 70/289, 10/697, 274/291 is

GCF of Numerators i.e. for 70,10,274 is 2

LCM of denominators i.e. for 289,697,291 is 3448059.

Thus, GCF of Fractions is 2/3448059.Finally, GCF of Fractions for 70/289, 10/697, 274/291 is 2/3448059.