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GCF of 262/314, 7037/500

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 262/314, 7037/500 i.e 1/78500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 262/314, 7037/500.

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 262/314,7037/500?

Given fractions are 262/314,7037/500

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 262/314,7037/500, numerators are 262,7037

Denominators are 314,500

The GCF of 262,7037 is 1 .

LCM of 314,500 is 78500.

The greatest common factor of 262/314,7037/500 = [GCF of 262,7037]/[LCM of 314,500]= 1/78500

Therefore, the GCF of 262/314,7037/500 is 1/78500.

Greatest Common Factor of 262,7037

To find the highest common factor of 262,7037, we have to find the factors of both numbers and list the highest common factor.

The factors of 262 are 1, 2, 131, 262

The factors of 7037 are 1, 31, 227, 7037

The HCF of 262,7037 is 1.

Lets's calculate GCF of 262,7037

Greatest Common Factor (GCF) of 262,7037 By Common Division

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

Greatest Common Factor of 262,7037 By Matching Biggest Common Factor Method

Greatest Common Factor of 262,7037 By Matching Biggest Common Factor Method

Now, list down the factors of 262

:

1,2,131,262

Now, list down the factors of 7037

:

1,31,227,7037

Greatest Common Factor

We found the factors 262,7037 . The biggest common factor number is the GCF number.
So the greatest common factor 262,7037 is 1.

Lets's calculate LCM of 314,500

Lowest Common Multiple of 314,500 using Common Division

2 314, 500
157, 250

∴ So the LCM of the given numbers is 2 x 157 x 250 = 78500

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/78500

Therefore, the GCF of Fractions 262/314,7037/500 is 1/78500

Least Common Multiple of 314,500 with GCF Formula

Least Common Multiple of 314,500 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 314,500 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,500) = 2

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

GCF(314,500) x common factors =2 x 1 = 2

LCM(314,500) = ( 314 × 500 ) / 2

LCM(314,500) = 157000 / 2

LCM(314,500) = 78500


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FAQs on GCF of Fractions of 262/314, 7037/500

1. What is the HCF of 262,7037?

The HCF of 262,7037 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 262/314, 7037/500?

Answer: GCF of Numerators as per given numbers 262/314, 7037/500 is

GCF of Numerators i.e. for 262,7037 is 1

LCM of denominators i.e. for 314,500 is 78500.

Thus, GCF of Fractions is 1/78500.Finally, GCF of Fractions for 262/314, 7037/500 is 1/78500.