How to Find GCF of 275/23, 828/466?

GCF of 275/23, 828/466

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 275/23, 828/466 i.e 1/10718 easily. The following is the detailed procedure to determine the greatest common factor of fractions 275/23, 828/466.

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 275/23,828/466?

Given fractions are 275/23,828/466

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 275/23,828/466, numerators are 275,828

Denominators are 23,466

The GCF of 275,828 is 1 .

LCM of 23,466 is 10718.

The greatest common factor of 275/23,828/466 = [GCF of 275,828]/[LCM of 23,466]= 1/10718

Therefore, the GCF of 275/23,828/466 is 1/10718.

Greatest Common Factor of 275,828

To find the highest common factor of 275,828, we have to find the factors of both numbers and list the highest common factor.

The factors of 275 are 1, 5, 11, 25, 55, 275

The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828

The HCF of 275,828 is 1.

Lets's calculate GCF of 275,828

Greatest Common Factor (GCF) of 275,828 By Common Division

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

Greatest Common Factor of 275,828 By Matching Biggest Common Factor Method

Now, list down the factors of 275

1,5,11,25,55,275

Now, list down the factors of 828

1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828

Greatest Common Factor

We found the factors 275,828 . The biggest common factor number is the GCF number.
So the greatest common factor 275,828 is 1.

Lets's calculate LCM of 23,466

Lowest Common Multiple of 23,466 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 10718

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10718

Therefore, the GCF of Fractions 275/23,828/466 is 1/10718

Least Common Multiple of 23,466 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 23,466 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,466) = 1

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

GCF(23,466) x common factors =1 x 1 = 1

LCM(23,466) = ( 23 × 466 ) / 1

LCM(23,466) = 10718 / 1

LCM(23,466) = 10718

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FAQs on GCF of Fractions of 275/23, 828/466

1. What is the HCF of 275,828?

The HCF of 275,828 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 275/23, 828/466?

Answer: GCF of Numerators as per given numbers 275/23, 828/466 is

GCF of Numerators i.e. for 275,828 is 1

LCM of denominators i.e. for 23,466 is 10718.

Thus, GCF of Fractions is 1/10718.Finally, GCF of Fractions for 275/23, 828/466 is 1/10718.