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GCF of 825/105, 575/719

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 825/105, 575/719 i.e 25/75495 easily. The following is the detailed procedure to determine the greatest common factor of fractions 825/105, 575/719.

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 825/105,575/719?

Given fractions are 825/105,575/719

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 825/105,575/719, numerators are 825,575

Denominators are 105,719

The GCF of 825,575 is 25 .

LCM of 105,719 is 75495.

The greatest common factor of 825/105,575/719 = [GCF of 825,575]/[LCM of 105,719]= 25/75495

Therefore, the GCF of 825/105,575/719 is 25/75495.

Greatest Common Factor of 825,575

To find the highest common factor of 825,575, 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 575 are 1, 5, 23, 25, 115, 575

The HCF of 825,575 is 25.

Lets's calculate GCF of 825,575

Greatest Common Factor (GCF) of 825,575 By Common Division

5 825, 575
5 165, 115
33, 23

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

Greatest Common Factor of 825,575 By Matching Biggest Common Factor Method

Greatest Common Factor of 825,575 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 575

:

1,5,23,25,115,575

Greatest Common Factor

We found the factors 825,575 . The biggest common factor number is the GCF number.
So the greatest common factor 825,575 is 25.

Lets's calculate LCM of 105,719

Lowest Common Multiple of 105,719 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 75495

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/75495

Therefore, the GCF of Fractions 825/105,575/719 is 25/75495

Least Common Multiple of 105,719 with GCF Formula

Least Common Multiple of 105,719 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 105,719 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(105,719) = 1

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

GCF(105,719) x common factors =1 x 1 = 1

LCM(105,719) = ( 105 × 719 ) / 1

LCM(105,719) = 75495 / 1

LCM(105,719) = 75495


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FAQs on GCF of Fractions of 825/105, 575/719

1. What is the HCF of 825,575?

The HCF of 825,575 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 825/105, 575/719?

Answer: GCF of Numerators as per given numbers 825/105, 575/719 is

GCF of Numerators i.e. for 825,575 is 25

LCM of denominators i.e. for 105,719 is 75495.

Thus, GCF of Fractions is 25/75495.Finally, GCF of Fractions for 825/105, 575/719 is 25/75495.