How to Find GCF of 5607/132, 8219/5664?

GCF of 5607/132, 8219/5664

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 5607/132, 8219/5664 i.e 1/62304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5607/132, 8219/5664.

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 5607/132,8219/5664?

Given fractions are 5607/132,8219/5664

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 5607/132,8219/5664, numerators are 5607,8219

Denominators are 132,5664

The GCF of 5607,8219 is 1 .

LCM of 132,5664 is 62304.

The greatest common factor of 5607/132,8219/5664 = [GCF of 5607,8219]/[LCM of 132,5664]= 1/62304

Therefore, the GCF of 5607/132,8219/5664 is 1/62304.

Greatest Common Factor of 5607,8219

To find the highest common factor of 5607,8219, we have to find the factors of both numbers and list the highest common factor.

The factors of 5607 are 1, 3, 7, 9, 21, 63, 89, 267, 623, 801, 1869, 5607

The factors of 8219 are 1, 8219

The HCF of 5607,8219 is 1.

Lets's calculate GCF of 5607,8219

Greatest Common Factor (GCF) of 5607,8219 By Common Division

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

Greatest Common Factor of 5607,8219 By Matching Biggest Common Factor Method

Now, list down the factors of 5607

1,3,7,9,21,63,89,267,623,801,1869,5607

Now, list down the factors of 8219

1,8219

Greatest Common Factor

We found the factors 5607,8219 . The biggest common factor number is the GCF number.
So the greatest common factor 5607,8219 is 1.

Lets's calculate LCM of 132,5664

Lowest Common Multiple of 132,5664 using Common Division

2	132, 5664
2	66, 2832
3	33, 1416
	11, 472

∴ So the LCM of the given numbers is 2 x 2 x 3 x 11 x 472 = 62304

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/62304

Therefore, the GCF of Fractions 5607/132,8219/5664 is 1/62304

Least Common Multiple of 132,5664 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 132,5664 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(132,5664) = 12

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

GCF(132,5664) x common factors =12 x 1 = 12

LCM(132,5664) = ( 132 × 5664 ) / 12

LCM(132,5664) = 747648 / 12

LCM(132,5664) = 62304

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 5607/132, 8219/5664

1. What is the HCF of 5607,8219?

The HCF of 5607,8219 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 5607/132, 8219/5664?

Answer: GCF of Numerators as per given numbers 5607/132, 8219/5664 is

GCF of Numerators i.e. for 5607,8219 is 1

LCM of denominators i.e. for 132,5664 is 62304.

Thus, GCF of Fractions is 1/62304.Finally, GCF of Fractions for 5607/132, 8219/5664 is 1/62304.