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GCF of 725/250, 150/217

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 725/250, 150/217 i.e 25/54250 easily. The following is the detailed procedure to determine the greatest common factor of fractions 725/250, 150/217.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 725/250,150/217?

Given fractions are 725/250,150/217

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 725/250,150/217, numerators are 725,150

Denominators are 250,217

The GCF of 725,150 is 25 .

LCM of 250,217 is 54250.

The greatest common factor of 725/250,150/217 = [GCF of 725,150]/[LCM of 250,217]= 25/54250

Therefore, the GCF of 725/250,150/217 is 25/54250.

Greatest Common Factor of 725,150

To find the highest common factor of 725,150, we have to find the factors of both numbers and list the highest common factor.

The factors of 725 are 1, 5, 25, 29, 145, 725

The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

The HCF of 725,150 is 25.

Lets's calculate GCF of 725,150

Greatest Common Factor (GCF) of 725,150 By Common Division

5 725, 150
5 145, 30
29, 6

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

Greatest Common Factor of 725,150 By Matching Biggest Common Factor Method

Greatest Common Factor of 725,150 By Matching Biggest Common Factor Method

Now, list down the factors of 725

:

1,5,25,29,145,725

Now, list down the factors of 150

:

1,2,3,5,6,10,15,25,30,50,75,150

Greatest Common Factor

We found the factors 725,150 . The biggest common factor number is the GCF number.
So the greatest common factor 725,150 is 25.

Lets's calculate LCM of 250,217

Lowest Common Multiple of 250,217 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 54250

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/54250

Therefore, the GCF of Fractions 725/250,150/217 is 25/54250

Least Common Multiple of 250,217 with GCF Formula

Least Common Multiple of 250,217 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 250,217 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(250,217) = 1

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

GCF(250,217) x common factors =1 x 1 = 1

LCM(250,217) = ( 250 × 217 ) / 1

LCM(250,217) = 54250 / 1

LCM(250,217) = 54250


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FAQs on GCF of Fractions of 725/250, 150/217

1. What is the HCF of 725,150?

The HCF of 725,150 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 725/250, 150/217?

Answer: GCF of Numerators as per given numbers 725/250, 150/217 is

GCF of Numerators i.e. for 725,150 is 25

LCM of denominators i.e. for 250,217 is 54250.

Thus, GCF of Fractions is 25/54250.Finally, GCF of Fractions for 725/250, 150/217 is 25/54250.