How to Find GCF of 561/120, 1664/856?

GCF of 561/120, 1664/856

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 561/120, 1664/856 i.e 1/12840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 561/120, 1664/856.

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 561/120,1664/856?

Given fractions are 561/120,1664/856

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 561/120,1664/856, numerators are 561,1664

Denominators are 120,856

The GCF of 561,1664 is 1 .

LCM of 120,856 is 12840.

The greatest common factor of 561/120,1664/856 = [GCF of 561,1664]/[LCM of 120,856]= 1/12840

Therefore, the GCF of 561/120,1664/856 is 1/12840.

Greatest Common Factor of 561,1664

To find the highest common factor of 561,1664, we have to find the factors of both numbers and list the highest common factor.

The factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561

The factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664

The HCF of 561,1664 is 1.

Lets's calculate GCF of 561,1664

Greatest Common Factor (GCF) of 561,1664 By Common Division

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

Greatest Common Factor of 561,1664 By Matching Biggest Common Factor Method

Now, list down the factors of 561

1,3,11,17,33,51,187,561

Now, list down the factors of 1664

1,2,4,8,13,16,26,32,52,64,104,128,208,416,832,1664

Greatest Common Factor

We found the factors 561,1664 . The biggest common factor number is the GCF number.
So the greatest common factor 561,1664 is 1.

Lets's calculate LCM of 120,856

Lowest Common Multiple of 120,856 using Common Division

2	120, 856
2	60, 428
2	30, 214
	15, 107

∴ So the LCM of the given numbers is 2 x 2 x 2 x 15 x 107 = 12840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12840

Therefore, the GCF of Fractions 561/120,1664/856 is 1/12840

Least Common Multiple of 120,856 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 120,856 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(120,856) = 8

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

GCF(120,856) x common factors =8 x 1 = 8

LCM(120,856) = ( 120 × 856 ) / 8

LCM(120,856) = 102720 / 8

LCM(120,856) = 12840

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 561/120, 1664/856

1. What is the HCF of 561,1664?

The HCF of 561,1664 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 561/120, 1664/856?

Answer: GCF of Numerators as per given numbers 561/120, 1664/856 is

GCF of Numerators i.e. for 561,1664 is 1

LCM of denominators i.e. for 120,856 is 12840.

Thus, GCF of Fractions is 1/12840.Finally, GCF of Fractions for 561/120, 1664/856 is 1/12840.