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GCF of 218/668, 105/228

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 218/668, 105/228 i.e 1/38076 easily. The following is the detailed procedure to determine the greatest common factor of fractions 218/668, 105/228.

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 218/668,105/228?

Given fractions are 218/668,105/228

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 218/668,105/228, numerators are 218,105

Denominators are 668,228

The GCF of 218,105 is 1 .

LCM of 668,228 is 38076.

The greatest common factor of 218/668,105/228 = [GCF of 218,105]/[LCM of 668,228]= 1/38076

Therefore, the GCF of 218/668,105/228 is 1/38076.

Greatest Common Factor of 218,105

To find the highest common factor of 218,105, we have to find the factors of both numbers and list the highest common factor.

The factors of 218 are 1, 2, 109, 218

The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105

The HCF of 218,105 is 1.

Lets's calculate GCF of 218,105

Greatest Common Factor (GCF) of 218,105 By Common Division

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

Greatest Common Factor of 218,105 By Matching Biggest Common Factor Method

Greatest Common Factor of 218,105 By Matching Biggest Common Factor Method

Now, list down the factors of 218

:

1,2,109,218

Now, list down the factors of 105

:

1,3,5,7,15,21,35,105

Greatest Common Factor

We found the factors 218,105 . The biggest common factor number is the GCF number.
So the greatest common factor 218,105 is 1.

Lets's calculate LCM of 668,228

Lowest Common Multiple of 668,228 using Common Division

2 668, 228
2 334, 114
167, 57

∴ So the LCM of the given numbers is 2 x 2 x 167 x 57 = 38076

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38076

Therefore, the GCF of Fractions 218/668,105/228 is 1/38076

Least Common Multiple of 668,228 with GCF Formula

Least Common Multiple of 668,228 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 668,228 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(668,228) = 4

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

GCF(668,228) x common factors =4 x 1 = 4

LCM(668,228) = ( 668 × 228 ) / 4

LCM(668,228) = 152304 / 4

LCM(668,228) = 38076


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FAQs on GCF of Fractions of 218/668, 105/228

1. What is the HCF of 218,105?

The HCF of 218,105 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 218/668, 105/228?

Answer: GCF of Numerators as per given numbers 218/668, 105/228 is

GCF of Numerators i.e. for 218,105 is 1

LCM of denominators i.e. for 668,228 is 38076.

Thus, GCF of Fractions is 1/38076.Finally, GCF of Fractions for 218/668, 105/228 is 1/38076.