How to Find GCF of 288/872, 9667/1676?

GCF of 288/872, 9667/1676

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 288/872, 9667/1676 i.e 1/365368 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/872, 9667/1676.

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 288/872,9667/1676?

Given fractions are 288/872,9667/1676

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 288/872,9667/1676, numerators are 288,9667

Denominators are 872,1676

The GCF of 288,9667 is 1 .

LCM of 872,1676 is 365368.

The greatest common factor of 288/872,9667/1676 = [GCF of 288,9667]/[LCM of 872,1676]= 1/365368

Therefore, the GCF of 288/872,9667/1676 is 1/365368.

Greatest Common Factor of 288,9667

To find the highest common factor of 288,9667, we have to find the factors of both numbers and list the highest common factor.

The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

The factors of 9667 are 1, 7, 1381, 9667

The HCF of 288,9667 is 1.

Lets's calculate GCF of 288,9667

Greatest Common Factor (GCF) of 288,9667 By Common Division

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

Greatest Common Factor of 288,9667 By Matching Biggest Common Factor Method

Now, list down the factors of 288

1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288

Now, list down the factors of 9667

1,7,1381,9667

Greatest Common Factor

We found the factors 288,9667 . The biggest common factor number is the GCF number.
So the greatest common factor 288,9667 is 1.

Lets's calculate LCM of 872,1676

Lowest Common Multiple of 872,1676 using Common Division

2	872, 1676
2	436, 838
	218, 419

∴ So the LCM of the given numbers is 2 x 2 x 218 x 419 = 365368

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/365368

Therefore, the GCF of Fractions 288/872,9667/1676 is 1/365368

Least Common Multiple of 872,1676 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 872,1676 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(872,1676) = 4

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

GCF(872,1676) x common factors =4 x 1 = 4

LCM(872,1676) = ( 872 × 1676 ) / 4

LCM(872,1676) = 1461472 / 4

LCM(872,1676) = 365368

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FAQs on GCF of Fractions of 288/872, 9667/1676

1. What is the HCF of 288,9667?

The HCF of 288,9667 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 288/872, 9667/1676?

Answer: GCF of Numerators as per given numbers 288/872, 9667/1676 is

GCF of Numerators i.e. for 288,9667 is 1

LCM of denominators i.e. for 872,1676 is 365368.

Thus, GCF of Fractions is 1/365368.Finally, GCF of Fractions for 288/872, 9667/1676 is 1/365368.