How to Find GCF of 442/209, 702/240?

GCF of 442/209, 702/240

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 442/209, 702/240 i.e 26/50160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 442/209, 702/240.

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 442/209,702/240?

Given fractions are 442/209,702/240

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 442/209,702/240, numerators are 442,702

Denominators are 209,240

The GCF of 442,702 is 26 .

LCM of 209,240 is 50160.

The greatest common factor of 442/209,702/240 = [GCF of 442,702]/[LCM of 209,240]= 26/50160

Therefore, the GCF of 442/209,702/240 is 26/50160.

Greatest Common Factor of 442,702

To find the highest common factor of 442,702, we have to find the factors of both numbers and list the highest common factor.

The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442

The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702

The HCF of 442,702 is 26.

Lets's calculate GCF of 442,702

Greatest Common Factor (GCF) of 442,702 By Common Division

2	442, 702
13	221, 351
	17, 27

∴ So the GCF of the given numbers is 2 x 13 = 26

Greatest Common Factor of 442,702 By Matching Biggest Common Factor Method

Now, list down the factors of 442

1,2,13,17,26,34,221,442

Now, list down the factors of 702

1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702

Greatest Common Factor

We found the factors 442,702 . The biggest common factor number is the GCF number.
So the greatest common factor 442,702 is 26.

Lets's calculate LCM of 209,240

Lowest Common Multiple of 209,240 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 50160

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/50160

Therefore, the GCF of Fractions 442/209,702/240 is 26/50160

Least Common Multiple of 209,240 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 209,240 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(209,240) = 1

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

GCF(209,240) x common factors =1 x 1 = 1

LCM(209,240) = ( 209 × 240 ) / 1

LCM(209,240) = 50160 / 1

LCM(209,240) = 50160

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FAQs on GCF of Fractions of 442/209, 702/240

1. What is the HCF of 442,702?

The HCF of 442,702 is 26

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 442/209, 702/240?

Answer: GCF of Numerators as per given numbers 442/209, 702/240 is

GCF of Numerators i.e. for 442,702 is 26

LCM of denominators i.e. for 209,240 is 50160.

Thus, GCF of Fractions is 26/50160.Finally, GCF of Fractions for 442/209, 702/240 is 26/50160.