How to Find GCF of 7575/609, 5609/2352?

GCF of 7575/609, 5609/2352

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 7575/609, 5609/2352 i.e 1/68208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7575/609, 5609/2352.

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 7575/609,5609/2352?

Given fractions are 7575/609,5609/2352

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 7575/609,5609/2352, numerators are 7575,5609

Denominators are 609,2352

The GCF of 7575,5609 is 1 .

LCM of 609,2352 is 68208.

The greatest common factor of 7575/609,5609/2352 = [GCF of 7575,5609]/[LCM of 609,2352]= 1/68208

Therefore, the GCF of 7575/609,5609/2352 is 1/68208.

Greatest Common Factor of 7575,5609

To find the highest common factor of 7575,5609, we have to find the factors of both numbers and list the highest common factor.

The factors of 7575 are 1, 3, 5, 15, 25, 75, 101, 303, 505, 1515, 2525, 7575

The factors of 5609 are 1, 71, 79, 5609

The HCF of 7575,5609 is 1.

Lets's calculate GCF of 7575,5609

Greatest Common Factor (GCF) of 7575,5609 By Common Division

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

Greatest Common Factor of 7575,5609 By Matching Biggest Common Factor Method

Now, list down the factors of 7575

1,3,5,15,25,75,101,303,505,1515,2525,7575

Now, list down the factors of 5609

1,71,79,5609

Greatest Common Factor

We found the factors 7575,5609 . The biggest common factor number is the GCF number.
So the greatest common factor 7575,5609 is 1.

Lets's calculate LCM of 609,2352

Lowest Common Multiple of 609,2352 using Common Division

3	609, 2352
7	203, 784
	29, 112

∴ So the LCM of the given numbers is 3 x 7 x 29 x 112 = 68208

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/68208

Therefore, the GCF of Fractions 7575/609,5609/2352 is 1/68208

Least Common Multiple of 609,2352 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 609,2352 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(609,2352) = 21

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

GCF(609,2352) x common factors =21 x 1 = 21

LCM(609,2352) = ( 609 × 2352 ) / 21

LCM(609,2352) = 1432368 / 21

LCM(609,2352) = 68208

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FAQs on GCF of Fractions of 7575/609, 5609/2352

1. What is the HCF of 7575,5609?

The HCF of 7575,5609 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 7575/609, 5609/2352?

Answer: GCF of Numerators as per given numbers 7575/609, 5609/2352 is

GCF of Numerators i.e. for 7575,5609 is 1

LCM of denominators i.e. for 609,2352 is 68208.

Thus, GCF of Fractions is 1/68208.Finally, GCF of Fractions for 7575/609, 5609/2352 is 1/68208.