How to Find GCF of 1229/278, 9664/6869?

GCF of 1229/278, 9664/6869

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 1229/278, 9664/6869 i.e 1/1909582 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1229/278, 9664/6869.

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 1229/278,9664/6869?

Given fractions are 1229/278,9664/6869

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 1229/278,9664/6869, numerators are 1229,9664

Denominators are 278,6869

The GCF of 1229,9664 is 1 .

LCM of 278,6869 is 1909582.

The greatest common factor of 1229/278,9664/6869 = [GCF of 1229,9664]/[LCM of 278,6869]= 1/1909582

Therefore, the GCF of 1229/278,9664/6869 is 1/1909582.

Greatest Common Factor of 1229,9664

To find the highest common factor of 1229,9664, we have to find the factors of both numbers and list the highest common factor.

The factors of 1229 are 1, 1229

The factors of 9664 are 1, 2, 4, 8, 16, 32, 64, 151, 302, 604, 1208, 2416, 4832, 9664

The HCF of 1229,9664 is 1.

Lets's calculate GCF of 1229,9664

Greatest Common Factor (GCF) of 1229,9664 By Common Division

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

Greatest Common Factor of 1229,9664 By Matching Biggest Common Factor Method

Now, list down the factors of 1229

1,1229

Now, list down the factors of 9664

1,2,4,8,16,32,64,151,302,604,1208,2416,4832,9664

Greatest Common Factor

We found the factors 1229,9664 . The biggest common factor number is the GCF number.
So the greatest common factor 1229,9664 is 1.

Lets's calculate LCM of 278,6869

Lowest Common Multiple of 278,6869 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1909582

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1909582

Therefore, the GCF of Fractions 1229/278,9664/6869 is 1/1909582

Least Common Multiple of 278,6869 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 278,6869 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(278,6869) = 1

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

GCF(278,6869) x common factors =1 x 1 = 1

LCM(278,6869) = ( 278 × 6869 ) / 1

LCM(278,6869) = 1909582 / 1

LCM(278,6869) = 1909582

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FAQs on GCF of Fractions of 1229/278, 9664/6869

1. What is the HCF of 1229,9664?

The HCF of 1229,9664 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 1229/278, 9664/6869?

Answer: GCF of Numerators as per given numbers 1229/278, 9664/6869 is

GCF of Numerators i.e. for 1229,9664 is 1

LCM of denominators i.e. for 278,6869 is 1909582.

Thus, GCF of Fractions is 1/1909582.Finally, GCF of Fractions for 1229/278, 9664/6869 is 1/1909582.