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GCF of 266/65, 969/724

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 266/65, 969/724 i.e 19/47060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 266/65, 969/724.

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 266/65,969/724?

Given fractions are 266/65,969/724

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 266/65,969/724, numerators are 266,969

Denominators are 65,724

The GCF of 266,969 is 19 .

LCM of 65,724 is 47060.

The greatest common factor of 266/65,969/724 = [GCF of 266,969]/[LCM of 65,724]= 19/47060

Therefore, the GCF of 266/65,969/724 is 19/47060.

Greatest Common Factor of 266,969

To find the highest common factor of 266,969, we have to find the factors of both numbers and list the highest common factor.

The factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266

The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969

The HCF of 266,969 is 19.

Lets's calculate GCF of 266,969

Greatest Common Factor (GCF) of 266,969 By Common Division

19 266, 969
14, 51

∴ So the GCF of the given numbers is 19 = 19

Greatest Common Factor of 266,969 By Matching Biggest Common Factor Method

Greatest Common Factor of 266,969 By Matching Biggest Common Factor Method

Now, list down the factors of 266

:

1,2,7,14,19,38,133,266

Now, list down the factors of 969

:

1,3,17,19,51,57,323,969

Greatest Common Factor

We found the factors 266,969 . The biggest common factor number is the GCF number.
So the greatest common factor 266,969 is 19.

Lets's calculate LCM of 65,724

Lowest Common Multiple of 65,724 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 47060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/47060

Therefore, the GCF of Fractions 266/65,969/724 is 19/47060

Least Common Multiple of 65,724 with GCF Formula

Least Common Multiple of 65,724 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 65,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,724) = 1

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

GCF(65,724) x common factors =1 x 1 = 1

LCM(65,724) = ( 65 × 724 ) / 1

LCM(65,724) = 47060 / 1

LCM(65,724) = 47060


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FAQs on GCF of Fractions of 266/65, 969/724

1. What is the HCF of 266,969?

The HCF of 266,969 is 19

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 266/65, 969/724?

Answer: GCF of Numerators as per given numbers 266/65, 969/724 is

GCF of Numerators i.e. for 266,969 is 19

LCM of denominators i.e. for 65,724 is 47060.

Thus, GCF of Fractions is 19/47060.Finally, GCF of Fractions for 266/65, 969/724 is 19/47060.