How to Find GCF of 7569/496, 8228/8417?

GCF of 7569/496, 8228/8417

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 7569/496, 8228/8417 i.e 1/4174832 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7569/496, 8228/8417.

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 7569/496,8228/8417?

Given fractions are 7569/496,8228/8417

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 7569/496,8228/8417, numerators are 7569,8228

Denominators are 496,8417

The GCF of 7569,8228 is 1 .

LCM of 496,8417 is 4174832.

The greatest common factor of 7569/496,8228/8417 = [GCF of 7569,8228]/[LCM of 496,8417]= 1/4174832

Therefore, the GCF of 7569/496,8228/8417 is 1/4174832.

Greatest Common Factor of 7569,8228

To find the highest common factor of 7569,8228, we have to find the factors of both numbers and list the highest common factor.

The factors of 7569 are 1, 3, 9, 29, 87, 261, 841, 2523, 7569

The factors of 8228 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 121, 187, 242, 374, 484, 748, 2057, 4114, 8228

The HCF of 7569,8228 is 1.

Lets's calculate GCF of 7569,8228

Greatest Common Factor (GCF) of 7569,8228 By Common Division

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

Greatest Common Factor of 7569,8228 By Matching Biggest Common Factor Method

Now, list down the factors of 7569

1,3,9,29,87,261,841,2523,7569

Now, list down the factors of 8228

1,2,4,11,17,22,34,44,68,121,187,242,374,484,748,2057,4114,8228

Greatest Common Factor

We found the factors 7569,8228 . The biggest common factor number is the GCF number.
So the greatest common factor 7569,8228 is 1.

Lets's calculate LCM of 496,8417

Lowest Common Multiple of 496,8417 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 4174832

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4174832

Therefore, the GCF of Fractions 7569/496,8228/8417 is 1/4174832

Least Common Multiple of 496,8417 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 496,8417 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(496,8417) = 1

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

GCF(496,8417) x common factors =1 x 1 = 1

LCM(496,8417) = ( 496 × 8417 ) / 1

LCM(496,8417) = 4174832 / 1

LCM(496,8417) = 4174832

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FAQs on GCF of Fractions of 7569/496, 8228/8417

1. What is the HCF of 7569,8228?

The HCF of 7569,8228 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 7569/496, 8228/8417?

Answer: GCF of Numerators as per given numbers 7569/496, 8228/8417 is

GCF of Numerators i.e. for 7569,8228 is 1

LCM of denominators i.e. for 496,8417 is 4174832.

Thus, GCF of Fractions is 1/4174832.Finally, GCF of Fractions for 7569/496, 8228/8417 is 1/4174832.