How to Find GCF of 216/992, 397/104?

GCF of 216/992, 397/104

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 216/992, 397/104 i.e 1/12896 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/992, 397/104.

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 216/992,397/104?

Given fractions are 216/992,397/104

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 216/992,397/104, numerators are 216,397

Denominators are 992,104

The GCF of 216,397 is 1 .

LCM of 992,104 is 12896.

The greatest common factor of 216/992,397/104 = [GCF of 216,397]/[LCM of 992,104]= 1/12896

Therefore, the GCF of 216/992,397/104 is 1/12896.

Greatest Common Factor of 216,397

To find the highest common factor of 216,397, we have to find the factors of both numbers and list the highest common factor.

The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

The factors of 397 are 1, 397

The HCF of 216,397 is 1.

Lets's calculate GCF of 216,397

Greatest Common Factor (GCF) of 216,397 By Common Division

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

Greatest Common Factor of 216,397 By Matching Biggest Common Factor Method

Now, list down the factors of 216

1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216

Now, list down the factors of 397

1,397

Greatest Common Factor

We found the factors 216,397 . The biggest common factor number is the GCF number.
So the greatest common factor 216,397 is 1.

Lets's calculate LCM of 992,104

Lowest Common Multiple of 992,104 using Common Division

2	992, 104
2	496, 52
2	248, 26
	124, 13

∴ So the LCM of the given numbers is 2 x 2 x 2 x 124 x 13 = 12896

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12896

Therefore, the GCF of Fractions 216/992,397/104 is 1/12896

Least Common Multiple of 992,104 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 992,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(992,104) = 8

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

GCF(992,104) x common factors =8 x 1 = 8

LCM(992,104) = ( 992 × 104 ) / 8

LCM(992,104) = 103168 / 8

LCM(992,104) = 12896

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FAQs on GCF of Fractions of 216/992, 397/104

1. What is the HCF of 216,397?

The HCF of 216,397 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 216/992, 397/104?

Answer: GCF of Numerators as per given numbers 216/992, 397/104 is

GCF of Numerators i.e. for 216,397 is 1

LCM of denominators i.e. for 992,104 is 12896.

Thus, GCF of Fractions is 1/12896.Finally, GCF of Fractions for 216/992, 397/104 is 1/12896.