How to Find GCF of 1412/198, 3684/7546?

GCF of 1412/198, 3684/7546

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 1412/198, 3684/7546 i.e 4/67914 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1412/198, 3684/7546.

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 1412/198,3684/7546?

Given fractions are 1412/198,3684/7546

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 1412/198,3684/7546, numerators are 1412,3684

Denominators are 198,7546

The GCF of 1412,3684 is 4 .

LCM of 198,7546 is 67914.

The greatest common factor of 1412/198,3684/7546 = [GCF of 1412,3684]/[LCM of 198,7546]= 4/67914

Therefore, the GCF of 1412/198,3684/7546 is 4/67914.

Greatest Common Factor of 1412,3684

To find the highest common factor of 1412,3684, we have to find the factors of both numbers and list the highest common factor.

The factors of 1412 are 1, 2, 4, 353, 706, 1412

The factors of 3684 are 1, 2, 3, 4, 6, 12, 307, 614, 921, 1228, 1842, 3684

The HCF of 1412,3684 is 4.

Lets's calculate GCF of 1412,3684

Greatest Common Factor (GCF) of 1412,3684 By Common Division

2	1412, 3684
2	706, 1842
	353, 921

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 1412,3684 By Matching Biggest Common Factor Method

Now, list down the factors of 1412

1,2,4,353,706,1412

Now, list down the factors of 3684

1,2,3,4,6,12,307,614,921,1228,1842,3684

Greatest Common Factor

We found the factors 1412,3684 . The biggest common factor number is the GCF number.
So the greatest common factor 1412,3684 is 4.

Lets's calculate LCM of 198,7546

Lowest Common Multiple of 198,7546 using Common Division

2	198, 7546
11	99, 3773
	9, 343

∴ So the LCM of the given numbers is 2 x 11 x 9 x 343 = 67914

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/67914

Therefore, the GCF of Fractions 1412/198,3684/7546 is 4/67914

Least Common Multiple of 198,7546 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 198,7546 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(198,7546) = 22

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

GCF(198,7546) x common factors =22 x 1 = 22

LCM(198,7546) = ( 198 × 7546 ) / 22

LCM(198,7546) = 1494108 / 22

LCM(198,7546) = 67914

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 1412/198, 3684/7546

1. What is the HCF of 1412,3684?

The HCF of 1412,3684 is 4

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 1412/198, 3684/7546?

Answer: GCF of Numerators as per given numbers 1412/198, 3684/7546 is

GCF of Numerators i.e. for 1412,3684 is 4

LCM of denominators i.e. for 198,7546 is 67914.

Thus, GCF of Fractions is 4/67914.Finally, GCF of Fractions for 1412/198, 3684/7546 is 4/67914.