How to Find GCF of 2075/298, 7075/3659?

GCF of 2075/298, 7075/3659

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 2075/298, 7075/3659 i.e 25/1090382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2075/298, 7075/3659.

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 2075/298,7075/3659?

Given fractions are 2075/298,7075/3659

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 2075/298,7075/3659, numerators are 2075,7075

Denominators are 298,3659

The GCF of 2075,7075 is 25 .

LCM of 298,3659 is 1090382.

The greatest common factor of 2075/298,7075/3659 = [GCF of 2075,7075]/[LCM of 298,3659]= 25/1090382

Therefore, the GCF of 2075/298,7075/3659 is 25/1090382.

Greatest Common Factor of 2075,7075

To find the highest common factor of 2075,7075, we have to find the factors of both numbers and list the highest common factor.

The factors of 2075 are 1, 5, 25, 83, 415, 2075

The factors of 7075 are 1, 5, 25, 283, 1415, 7075

The HCF of 2075,7075 is 25.

Lets's calculate GCF of 2075,7075

Greatest Common Factor (GCF) of 2075,7075 By Common Division

5	2075, 7075
5	415, 1415
	83, 283

∴ So the GCF of the given numbers is 5 x 5 = 25

Greatest Common Factor of 2075,7075 By Matching Biggest Common Factor Method

Now, list down the factors of 2075

1,5,25,83,415,2075

Now, list down the factors of 7075

1,5,25,283,1415,7075

Greatest Common Factor

We found the factors 2075,7075 . The biggest common factor number is the GCF number.
So the greatest common factor 2075,7075 is 25.

Lets's calculate LCM of 298,3659

Lowest Common Multiple of 298,3659 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1090382

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/1090382

Therefore, the GCF of Fractions 2075/298,7075/3659 is 25/1090382

Least Common Multiple of 298,3659 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 298,3659 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(298,3659) = 1

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

GCF(298,3659) x common factors =1 x 1 = 1

LCM(298,3659) = ( 298 × 3659 ) / 1

LCM(298,3659) = 1090382 / 1

LCM(298,3659) = 1090382

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FAQs on GCF of Fractions of 2075/298, 7075/3659

1. What is the HCF of 2075,7075?

The HCF of 2075,7075 is 25

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 2075/298, 7075/3659?

Answer: GCF of Numerators as per given numbers 2075/298, 7075/3659 is

GCF of Numerators i.e. for 2075,7075 is 25

LCM of denominators i.e. for 298,3659 is 1090382.

Thus, GCF of Fractions is 25/1090382.Finally, GCF of Fractions for 2075/298, 7075/3659 is 25/1090382.