How to Find GCF of 217/448, 4098/536?

GCF of 217/448, 4098/536

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 217/448, 4098/536 i.e 1/30016 easily. The following is the detailed procedure to determine the greatest common factor of fractions 217/448, 4098/536.

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 217/448,4098/536?

Given fractions are 217/448,4098/536

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 217/448,4098/536, numerators are 217,4098

Denominators are 448,536

The GCF of 217,4098 is 1 .

LCM of 448,536 is 30016.

The greatest common factor of 217/448,4098/536 = [GCF of 217,4098]/[LCM of 448,536]= 1/30016

Therefore, the GCF of 217/448,4098/536 is 1/30016.

Greatest Common Factor of 217,4098

To find the highest common factor of 217,4098, we have to find the factors of both numbers and list the highest common factor.

The factors of 217 are 1, 7, 31, 217

The factors of 4098 are 1, 2, 3, 6, 683, 1366, 2049, 4098

The HCF of 217,4098 is 1.

Lets's calculate GCF of 217,4098

Greatest Common Factor (GCF) of 217,4098 By Common Division

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

Greatest Common Factor of 217,4098 By Matching Biggest Common Factor Method

Now, list down the factors of 217

1,7,31,217

Now, list down the factors of 4098

1,2,3,6,683,1366,2049,4098

Greatest Common Factor

We found the factors 217,4098 . The biggest common factor number is the GCF number.
So the greatest common factor 217,4098 is 1.

Lets's calculate LCM of 448,536

Lowest Common Multiple of 448,536 using Common Division

2	448, 536
2	224, 268
2	112, 134
	56, 67

∴ So the LCM of the given numbers is 2 x 2 x 2 x 56 x 67 = 30016

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30016

Therefore, the GCF of Fractions 217/448,4098/536 is 1/30016

Least Common Multiple of 448,536 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 448,536 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(448,536) = 8

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

GCF(448,536) x common factors =8 x 1 = 8

LCM(448,536) = ( 448 × 536 ) / 8

LCM(448,536) = 240128 / 8

LCM(448,536) = 30016

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FAQs on GCF of Fractions of 217/448, 4098/536

1. What is the HCF of 217,4098?

The HCF of 217,4098 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 217/448, 4098/536?

Answer: GCF of Numerators as per given numbers 217/448, 4098/536 is

GCF of Numerators i.e. for 217,4098 is 1

LCM of denominators i.e. for 448,536 is 30016.

Thus, GCF of Fractions is 1/30016.Finally, GCF of Fractions for 217/448, 4098/536 is 1/30016.