How to Find GCF of 1531/726, 8509/1234?

GCF of 1531/726, 8509/1234

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 1531/726, 8509/1234 i.e 1/447942 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1531/726, 8509/1234.

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 1531/726,8509/1234?

Given fractions are 1531/726,8509/1234

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 1531/726,8509/1234, numerators are 1531,8509

Denominators are 726,1234

The GCF of 1531,8509 is 1 .

LCM of 726,1234 is 447942.

The greatest common factor of 1531/726,8509/1234 = [GCF of 1531,8509]/[LCM of 726,1234]= 1/447942

Therefore, the GCF of 1531/726,8509/1234 is 1/447942.

Greatest Common Factor of 1531,8509

To find the highest common factor of 1531,8509, we have to find the factors of both numbers and list the highest common factor.

The factors of 1531 are 1, 1531

The factors of 8509 are 1, 67, 127, 8509

The HCF of 1531,8509 is 1.

Lets's calculate GCF of 1531,8509

Greatest Common Factor (GCF) of 1531,8509 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 1531,8509 By Matching Biggest Common Factor Method

Now, list down the factors of 1531

1,1531

Now, list down the factors of 8509

1,67,127,8509

Greatest Common Factor

We found the factors 1531,8509 . The biggest common factor number is the GCF number.
So the greatest common factor 1531,8509 is 1.

Lets's calculate LCM of 726,1234

Lowest Common Multiple of 726,1234 using Common Division

2	726, 1234
	363, 617

∴ So the LCM of the given numbers is 2 x 363 x 617 = 447942

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/447942

Therefore, the GCF of Fractions 1531/726,8509/1234 is 1/447942

Least Common Multiple of 726,1234 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 726,1234 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(726,1234) = 2

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

GCF(726,1234) x common factors =2 x 1 = 2

LCM(726,1234) = ( 726 × 1234 ) / 2

LCM(726,1234) = 895884 / 2

LCM(726,1234) = 447942

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 1531/726, 8509/1234

1. What is the HCF of 1531,8509?

The HCF of 1531,8509 is 1

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 1531/726, 8509/1234?

Answer: GCF of Numerators as per given numbers 1531/726, 8509/1234 is

GCF of Numerators i.e. for 1531,8509 is 1

LCM of denominators i.e. for 726,1234 is 447942.

Thus, GCF of Fractions is 1/447942.Finally, GCF of Fractions for 1531/726, 8509/1234 is 1/447942.