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GCF of 749/824, 198/900

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 749/824, 198/900 i.e 1/185400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 749/824, 198/900.

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 749/824,198/900?

Given fractions are 749/824,198/900

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 749/824,198/900, numerators are 749,198

Denominators are 824,900

The GCF of 749,198 is 1 .

LCM of 824,900 is 185400.

The greatest common factor of 749/824,198/900 = [GCF of 749,198]/[LCM of 824,900]= 1/185400

Therefore, the GCF of 749/824,198/900 is 1/185400.

Greatest Common Factor of 749,198

To find the highest common factor of 749,198, we have to find the factors of both numbers and list the highest common factor.

The factors of 749 are 1, 7, 107, 749

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198

The HCF of 749,198 is 1.

Lets's calculate GCF of 749,198

Greatest Common Factor (GCF) of 749,198 By Common Division

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

Greatest Common Factor of 749,198 By Matching Biggest Common Factor Method

Greatest Common Factor of 749,198 By Matching Biggest Common Factor Method

Now, list down the factors of 749

:

1,7,107,749

Now, list down the factors of 198

:

1,2,3,6,9,11,18,22,33,66,99,198

Greatest Common Factor

We found the factors 749,198 . The biggest common factor number is the GCF number.
So the greatest common factor 749,198 is 1.

Lets's calculate LCM of 824,900

Lowest Common Multiple of 824,900 using Common Division

2 824, 900
2 412, 450
206, 225

∴ So the LCM of the given numbers is 2 x 2 x 206 x 225 = 185400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/185400

Therefore, the GCF of Fractions 749/824,198/900 is 1/185400

Least Common Multiple of 824,900 with GCF Formula

Least Common Multiple of 824,900 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 824,900 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(824,900) = 4

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

GCF(824,900) x common factors =4 x 1 = 4

LCM(824,900) = ( 824 × 900 ) / 4

LCM(824,900) = 741600 / 4

LCM(824,900) = 185400


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FAQs on GCF of Fractions of 749/824, 198/900

1. What is the HCF of 749,198?

The HCF of 749,198 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 749/824, 198/900?

Answer: GCF of Numerators as per given numbers 749/824, 198/900 is

GCF of Numerators i.e. for 749,198 is 1

LCM of denominators i.e. for 824,900 is 185400.

Thus, GCF of Fractions is 1/185400.Finally, GCF of Fractions for 749/824, 198/900 is 1/185400.