How to Find GCF of 1992/168, 8562/706?

GCF of 1992/168, 8562/706

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 1992/168, 8562/706 i.e 6/59304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1992/168, 8562/706.

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 1992/168,8562/706?

Given fractions are 1992/168,8562/706

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 1992/168,8562/706, numerators are 1992,8562

Denominators are 168,706

The GCF of 1992,8562 is 6 .

LCM of 168,706 is 59304.

The greatest common factor of 1992/168,8562/706 = [GCF of 1992,8562]/[LCM of 168,706]= 6/59304

Therefore, the GCF of 1992/168,8562/706 is 6/59304.

Greatest Common Factor of 1992,8562

To find the highest common factor of 1992,8562, we have to find the factors of both numbers and list the highest common factor.

The factors of 1992 are 1, 2, 3, 4, 6, 8, 12, 24, 83, 166, 249, 332, 498, 664, 996, 1992

The factors of 8562 are 1, 2, 3, 6, 1427, 2854, 4281, 8562

The HCF of 1992,8562 is 6.

Lets's calculate GCF of 1992,8562

Greatest Common Factor (GCF) of 1992,8562 By Common Division

2	1992, 8562
3	996, 4281
	332, 1427

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 1992,8562 By Matching Biggest Common Factor Method

Now, list down the factors of 1992

1,2,3,4,6,8,12,24,83,166,249,332,498,664,996,1992

Now, list down the factors of 8562

1,2,3,6,1427,2854,4281,8562

Greatest Common Factor

We found the factors 1992,8562 . The biggest common factor number is the GCF number.
So the greatest common factor 1992,8562 is 6.

Lets's calculate LCM of 168,706

Lowest Common Multiple of 168,706 using Common Division

2	168, 706
	84, 353

∴ So the LCM of the given numbers is 2 x 84 x 353 = 59304

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/59304

Therefore, the GCF of Fractions 1992/168,8562/706 is 6/59304

Least Common Multiple of 168,706 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 168,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(168,706) = 2

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

GCF(168,706) x common factors =2 x 1 = 2

LCM(168,706) = ( 168 × 706 ) / 2

LCM(168,706) = 118608 / 2

LCM(168,706) = 59304

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 1992/168, 8562/706

1. What is the HCF of 1992,8562?

The HCF of 1992,8562 is 6

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 1992/168, 8562/706?

Answer: GCF of Numerators as per given numbers 1992/168, 8562/706 is

GCF of Numerators i.e. for 1992,8562 is 6

LCM of denominators i.e. for 168,706 is 59304.

Thus, GCF of Fractions is 6/59304.Finally, GCF of Fractions for 1992/168, 8562/706 is 6/59304.