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GCF of 171/69, 280/749

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 171/69, 280/749 i.e 1/51681 easily. The following is the detailed procedure to determine the greatest common factor of fractions 171/69, 280/749.

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 171/69,280/749?

Given fractions are 171/69,280/749

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 171/69,280/749, numerators are 171,280

Denominators are 69,749

The GCF of 171,280 is 1 .

LCM of 69,749 is 51681.

The greatest common factor of 171/69,280/749 = [GCF of 171,280]/[LCM of 69,749]= 1/51681

Therefore, the GCF of 171/69,280/749 is 1/51681.

Greatest Common Factor of 171,280

To find the highest common factor of 171,280, we have to find the factors of both numbers and list the highest common factor.

The factors of 171 are 1, 3, 9, 19, 57, 171

The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280

The HCF of 171,280 is 1.

Lets's calculate GCF of 171,280

Greatest Common Factor (GCF) of 171,280 By Common Division

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

Greatest Common Factor of 171,280 By Matching Biggest Common Factor Method

Greatest Common Factor of 171,280 By Matching Biggest Common Factor Method

Now, list down the factors of 171

:

1,3,9,19,57,171

Now, list down the factors of 280

:

1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280

Greatest Common Factor

We found the factors 171,280 . The biggest common factor number is the GCF number.
So the greatest common factor 171,280 is 1.

Lets's calculate LCM of 69,749

Lowest Common Multiple of 69,749 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 51681

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/51681

Therefore, the GCF of Fractions 171/69,280/749 is 1/51681

Least Common Multiple of 69,749 with GCF Formula

Least Common Multiple of 69,749 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 69,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(69,749) = 1

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

GCF(69,749) x common factors =1 x 1 = 1

LCM(69,749) = ( 69 × 749 ) / 1

LCM(69,749) = 51681 / 1

LCM(69,749) = 51681


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FAQs on GCF of Fractions of 171/69, 280/749

1. What is the HCF of 171,280?

The HCF of 171,280 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 171/69, 280/749?

Answer: GCF of Numerators as per given numbers 171/69, 280/749 is

GCF of Numerators i.e. for 171,280 is 1

LCM of denominators i.e. for 69,749 is 51681.

Thus, GCF of Fractions is 1/51681.Finally, GCF of Fractions for 171/69, 280/749 is 1/51681.