How to Find GCF of 825/78, 425/3643?

GCF of 825/78, 425/3643

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 825/78, 425/3643 i.e 25/284154 easily. The following is the detailed procedure to determine the greatest common factor of fractions 825/78, 425/3643.

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 825/78,425/3643?

Given fractions are 825/78,425/3643

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 825/78,425/3643, numerators are 825,425

Denominators are 78,3643

The GCF of 825,425 is 25 .

LCM of 78,3643 is 284154.

The greatest common factor of 825/78,425/3643 = [GCF of 825,425]/[LCM of 78,3643]= 25/284154

Therefore, the GCF of 825/78,425/3643 is 25/284154.

Greatest Common Factor of 825,425

To find the highest common factor of 825,425, we have to find the factors of both numbers and list the highest common factor.

The factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825

The factors of 425 are 1, 5, 17, 25, 85, 425

The HCF of 825,425 is 25.

Lets's calculate GCF of 825,425

Greatest Common Factor (GCF) of 825,425 By Common Division

5	825, 425
5	165, 85
	33, 17

∴ So the GCF of the given numbers is 5 x 5 = 25

Greatest Common Factor of 825,425 By Matching Biggest Common Factor Method

Now, list down the factors of 825

1,3,5,11,15,25,33,55,75,165,275,825

Now, list down the factors of 425

1,5,17,25,85,425

Greatest Common Factor

We found the factors 825,425 . The biggest common factor number is the GCF number.
So the greatest common factor 825,425 is 25.

Lets's calculate LCM of 78,3643

Lowest Common Multiple of 78,3643 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 284154

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/284154

Therefore, the GCF of Fractions 825/78,425/3643 is 25/284154

Least Common Multiple of 78,3643 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 78,3643 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,3643) = 1

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

GCF(78,3643) x common factors =1 x 1 = 1

LCM(78,3643) = ( 78 × 3643 ) / 1

LCM(78,3643) = 284154 / 1

LCM(78,3643) = 284154

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FAQs on GCF of Fractions of 825/78, 425/3643

1. What is the HCF of 825,425?

The HCF of 825,425 is 25

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 825/78, 425/3643?

Answer: GCF of Numerators as per given numbers 825/78, 425/3643 is

GCF of Numerators i.e. for 825,425 is 25

LCM of denominators i.e. for 78,3643 is 284154.

Thus, GCF of Fractions is 25/284154.Finally, GCF of Fractions for 825/78, 425/3643 is 25/284154.