How to Find GCF of 830/914, 669/869?

GCF of 830/914, 669/869

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 830/914, 669/869 i.e 1/794266 easily. The following is the detailed procedure to determine the greatest common factor of fractions 830/914, 669/869.

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 830/914,669/869?

Given fractions are 830/914,669/869

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 830/914,669/869, numerators are 830,669

Denominators are 914,869

The GCF of 830,669 is 1 .

LCM of 914,869 is 794266.

The greatest common factor of 830/914,669/869 = [GCF of 830,669]/[LCM of 914,869]= 1/794266

Therefore, the GCF of 830/914,669/869 is 1/794266.

Greatest Common Factor of 830,669

To find the highest common factor of 830,669, we have to find the factors of both numbers and list the highest common factor.

The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830

The factors of 669 are 1, 3, 223, 669

The HCF of 830,669 is 1.

Lets's calculate GCF of 830,669

Greatest Common Factor (GCF) of 830,669 By Common Division

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

Greatest Common Factor of 830,669 By Matching Biggest Common Factor Method

Now, list down the factors of 830

1,2,5,10,83,166,415,830

Now, list down the factors of 669

1,3,223,669

Greatest Common Factor

We found the factors 830,669 . The biggest common factor number is the GCF number.
So the greatest common factor 830,669 is 1.

Lets's calculate LCM of 914,869

Lowest Common Multiple of 914,869 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 794266

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/794266

Therefore, the GCF of Fractions 830/914,669/869 is 1/794266

Least Common Multiple of 914,869 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 914,869 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(914,869) = 1

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

GCF(914,869) x common factors =1 x 1 = 1

LCM(914,869) = ( 914 × 869 ) / 1

LCM(914,869) = 794266 / 1

LCM(914,869) = 794266

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FAQs on GCF of Fractions of 830/914, 669/869

1. What is the HCF of 830,669?

The HCF of 830,669 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 830/914, 669/869?

Answer: GCF of Numerators as per given numbers 830/914, 669/869 is

GCF of Numerators i.e. for 830,669 is 1

LCM of denominators i.e. for 914,869 is 794266.

Thus, GCF of Fractions is 1/794266.Finally, GCF of Fractions for 830/914, 669/869 is 1/794266.