How to Find GCF of 417/364, 9227/1948?

GCF of 417/364, 9227/1948

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 417/364, 9227/1948 i.e 1/177268 easily. The following is the detailed procedure to determine the greatest common factor of fractions 417/364, 9227/1948.

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 417/364,9227/1948?

Given fractions are 417/364,9227/1948

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 417/364,9227/1948, numerators are 417,9227

Denominators are 364,1948

The GCF of 417,9227 is 1 .

LCM of 364,1948 is 177268.

The greatest common factor of 417/364,9227/1948 = [GCF of 417,9227]/[LCM of 364,1948]= 1/177268

Therefore, the GCF of 417/364,9227/1948 is 1/177268.

Greatest Common Factor of 417,9227

To find the highest common factor of 417,9227, we have to find the factors of both numbers and list the highest common factor.

The factors of 417 are 1, 3, 139, 417

The factors of 9227 are 1, 9227

The HCF of 417,9227 is 1.

Lets's calculate GCF of 417,9227

Greatest Common Factor (GCF) of 417,9227 By Common Division

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

Greatest Common Factor of 417,9227 By Matching Biggest Common Factor Method

Now, list down the factors of 417

1,3,139,417

Now, list down the factors of 9227

1,9227

Greatest Common Factor

We found the factors 417,9227 . The biggest common factor number is the GCF number.
So the greatest common factor 417,9227 is 1.

Lets's calculate LCM of 364,1948

Lowest Common Multiple of 364,1948 using Common Division

2	364, 1948
2	182, 974
	91, 487

∴ So the LCM of the given numbers is 2 x 2 x 91 x 487 = 177268

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/177268

Therefore, the GCF of Fractions 417/364,9227/1948 is 1/177268

Least Common Multiple of 364,1948 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 364,1948 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(364,1948) = 4

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

GCF(364,1948) x common factors =4 x 1 = 4

LCM(364,1948) = ( 364 × 1948 ) / 4

LCM(364,1948) = 709072 / 4

LCM(364,1948) = 177268

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FAQs on GCF of Fractions of 417/364, 9227/1948

1. What is the HCF of 417,9227?

The HCF of 417,9227 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 417/364, 9227/1948?

Answer: GCF of Numerators as per given numbers 417/364, 9227/1948 is

GCF of Numerators i.e. for 417,9227 is 1

LCM of denominators i.e. for 364,1948 is 177268.

Thus, GCF of Fractions is 1/177268.Finally, GCF of Fractions for 417/364, 9227/1948 is 1/177268.