How to Find GCF of 969/269, 3400/8833?

GCF of 969/269, 3400/8833

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 969/269, 3400/8833 i.e 17/2376077 easily. The following is the detailed procedure to determine the greatest common factor of fractions 969/269, 3400/8833.

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 969/269,3400/8833?

Given fractions are 969/269,3400/8833

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 969/269,3400/8833, numerators are 969,3400

Denominators are 269,8833

The GCF of 969,3400 is 17 .

LCM of 269,8833 is 2376077.

The greatest common factor of 969/269,3400/8833 = [GCF of 969,3400]/[LCM of 269,8833]= 17/2376077

Therefore, the GCF of 969/269,3400/8833 is 17/2376077.

Greatest Common Factor of 969,3400

To find the highest common factor of 969,3400, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 3400 are 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400

The HCF of 969,3400 is 17.

Lets's calculate GCF of 969,3400

Greatest Common Factor (GCF) of 969,3400 By Common Division

17	969, 3400
	57, 200

∴ So the GCF of the given numbers is 17 = 17

Greatest Common Factor of 969,3400 By Matching Biggest Common Factor Method

Now, list down the factors of 969

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

Now, list down the factors of 3400

1,2,4,5,8,10,17,20,25,34,40,50,68,85,100,136,170,200,340,425,680,850,1700,3400

Greatest Common Factor

We found the factors 969,3400 . The biggest common factor number is the GCF number.
So the greatest common factor 969,3400 is 17.

Lets's calculate LCM of 269,8833

Lowest Common Multiple of 269,8833 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2376077

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/2376077

Therefore, the GCF of Fractions 969/269,3400/8833 is 17/2376077

Least Common Multiple of 269,8833 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 269,8833 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(269,8833) = 1

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

GCF(269,8833) x common factors =1 x 1 = 1

LCM(269,8833) = ( 269 × 8833 ) / 1

LCM(269,8833) = 2376077 / 1

LCM(269,8833) = 2376077

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FAQs on GCF of Fractions of 969/269, 3400/8833

1. What is the HCF of 969,3400?

The HCF of 969,3400 is 17

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 969/269, 3400/8833?

Answer: GCF of Numerators as per given numbers 969/269, 3400/8833 is

GCF of Numerators i.e. for 969,3400 is 17

LCM of denominators i.e. for 269,8833 is 2376077.

Thus, GCF of Fractions is 17/2376077.Finally, GCF of Fractions for 969/269, 3400/8833 is 17/2376077.