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GCF of 278/17, 267/499

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 278/17, 267/499 i.e 1/8483 easily. The following is the detailed procedure to determine the greatest common factor of fractions 278/17, 267/499.

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 278/17,267/499?

Given fractions are 278/17,267/499

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 278/17,267/499, numerators are 278,267

Denominators are 17,499

The GCF of 278,267 is 1 .

LCM of 17,499 is 8483.

The greatest common factor of 278/17,267/499 = [GCF of 278,267]/[LCM of 17,499]= 1/8483

Therefore, the GCF of 278/17,267/499 is 1/8483.

Greatest Common Factor of 278,267

To find the highest common factor of 278,267, we have to find the factors of both numbers and list the highest common factor.

The factors of 278 are 1, 2, 139, 278

The factors of 267 are 1, 3, 89, 267

The HCF of 278,267 is 1.

Lets's calculate GCF of 278,267

Greatest Common Factor (GCF) of 278,267 By Common Division

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

Greatest Common Factor of 278,267 By Matching Biggest Common Factor Method

Greatest Common Factor of 278,267 By Matching Biggest Common Factor Method

Now, list down the factors of 278

:

1,2,139,278

Now, list down the factors of 267

:

1,3,89,267

Greatest Common Factor

We found the factors 278,267 . The biggest common factor number is the GCF number.
So the greatest common factor 278,267 is 1.


Lets's calculate LCM of 17,499

Lowest Common Multiple of 17,499 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 8483

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8483

Therefore, the GCF of Fractions 278/17,267/499 is 1/8483

Least Common Multiple of 17,499 with GCF Formula

Least Common Multiple of 17,499 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 17,499 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,499) = 1

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

GCF(17,499) x common factors =1 x 1 = 1

LCM(17,499) = ( 17 × 499 ) / 1

LCM(17,499) = 8483 / 1

LCM(17,499) = 8483


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 278/17, 267/499

1. What is the HCF of 278,267?

The HCF of 278,267 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 278/17, 267/499?

Answer: GCF of Numerators as per given numbers 278/17, 267/499 is

GCF of Numerators i.e. for 278,267 is 1

LCM of denominators i.e. for 17,499 is 8483.

Thus, GCF of Fractions is 1/8483.Finally, GCF of Fractions for 278/17, 267/499 is 1/8483.