How to Find GCF of 1682/476, 1978/8184?

GCF of 1682/476, 1978/8184

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 1682/476, 1978/8184 i.e 2/973896 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1682/476, 1978/8184.

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 1682/476,1978/8184?

Given fractions are 1682/476,1978/8184

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 1682/476,1978/8184, numerators are 1682,1978

Denominators are 476,8184

The GCF of 1682,1978 is 2 .

LCM of 476,8184 is 973896.

The greatest common factor of 1682/476,1978/8184 = [GCF of 1682,1978]/[LCM of 476,8184]= 2/973896

Therefore, the GCF of 1682/476,1978/8184 is 2/973896.

Greatest Common Factor of 1682,1978

To find the highest common factor of 1682,1978, we have to find the factors of both numbers and list the highest common factor.

The factors of 1682 are 1, 2, 29, 58, 841, 1682

The factors of 1978 are 1, 2, 23, 43, 46, 86, 989, 1978

The HCF of 1682,1978 is 2.

Lets's calculate GCF of 1682,1978

Greatest Common Factor (GCF) of 1682,1978 By Common Division

2	1682, 1978
	841, 989

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

Greatest Common Factor of 1682,1978 By Matching Biggest Common Factor Method

Now, list down the factors of 1682

1,2,29,58,841,1682

Now, list down the factors of 1978

1,2,23,43,46,86,989,1978

Greatest Common Factor

We found the factors 1682,1978 . The biggest common factor number is the GCF number.
So the greatest common factor 1682,1978 is 2.

Lets's calculate LCM of 476,8184

Lowest Common Multiple of 476,8184 using Common Division

2	476, 8184
2	238, 4092
	119, 2046

∴ So the LCM of the given numbers is 2 x 2 x 119 x 2046 = 973896

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/973896

Therefore, the GCF of Fractions 1682/476,1978/8184 is 2/973896

Least Common Multiple of 476,8184 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 476,8184 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(476,8184) = 4

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

GCF(476,8184) x common factors =4 x 1 = 4

LCM(476,8184) = ( 476 × 8184 ) / 4

LCM(476,8184) = 3895584 / 4

LCM(476,8184) = 973896

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FAQs on GCF of Fractions of 1682/476, 1978/8184

1. What is the HCF of 1682,1978?

The HCF of 1682,1978 is 2

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 1682/476, 1978/8184?

Answer: GCF of Numerators as per given numbers 1682/476, 1978/8184 is

GCF of Numerators i.e. for 1682,1978 is 2

LCM of denominators i.e. for 476,8184 is 973896.

Thus, GCF of Fractions is 2/973896.Finally, GCF of Fractions for 1682/476, 1978/8184 is 2/973896.