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GCF of 564/29, 609/945

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 564/29, 609/945 i.e 3/27405 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/29, 609/945.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 564/29,609/945?

Given fractions are 564/29,609/945

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 564/29,609/945, numerators are 564,609

Denominators are 29,945

The GCF of 564,609 is 3 .

LCM of 29,945 is 27405.

The greatest common factor of 564/29,609/945 = [GCF of 564,609]/[LCM of 29,945]= 3/27405

Therefore, the GCF of 564/29,609/945 is 3/27405.

Greatest Common Factor of 564,609

To find the highest common factor of 564,609, we have to find the factors of both numbers and list the highest common factor.

The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564

The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609

The HCF of 564,609 is 3.

Lets's calculate GCF of 564,609

Greatest Common Factor (GCF) of 564,609 By Common Division

3 564, 609
188, 203

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 564,609 By Matching Biggest Common Factor Method

Greatest Common Factor of 564,609 By Matching Biggest Common Factor Method

Now, list down the factors of 564

:

1,2,3,4,6,12,47,94,141,188,282,564

Now, list down the factors of 609

:

1,3,7,21,29,87,203,609

Greatest Common Factor

We found the factors 564,609 . The biggest common factor number is the GCF number.
So the greatest common factor 564,609 is 3.

Lets's calculate LCM of 29,945

Lowest Common Multiple of 29,945 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 27405

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/27405

Therefore, the GCF of Fractions 564/29,609/945 is 3/27405

Least Common Multiple of 29,945 with GCF Formula

Least Common Multiple of 29,945 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 29,945 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(29,945) = 1

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

GCF(29,945) x common factors =1 x 1 = 1

LCM(29,945) = ( 29 × 945 ) / 1

LCM(29,945) = 27405 / 1

LCM(29,945) = 27405


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FAQs on GCF of Fractions of 564/29, 609/945

1. What is the HCF of 564,609?

The HCF of 564,609 is 3

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 564/29, 609/945?

Answer: GCF of Numerators as per given numbers 564/29, 609/945 is

GCF of Numerators i.e. for 564,609 is 3

LCM of denominators i.e. for 29,945 is 27405.

Thus, GCF of Fractions is 3/27405.Finally, GCF of Fractions for 564/29, 609/945 is 3/27405.