How to Find GCF of 1683/676, 3686/5964?

GCF of 1683/676, 3686/5964

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 1683/676, 3686/5964 i.e 1/1007916 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1683/676, 3686/5964.

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 1683/676,3686/5964?

Given fractions are 1683/676,3686/5964

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 1683/676,3686/5964, numerators are 1683,3686

Denominators are 676,5964

The GCF of 1683,3686 is 1 .

LCM of 676,5964 is 1007916.

The greatest common factor of 1683/676,3686/5964 = [GCF of 1683,3686]/[LCM of 676,5964]= 1/1007916

Therefore, the GCF of 1683/676,3686/5964 is 1/1007916.

Greatest Common Factor of 1683,3686

To find the highest common factor of 1683,3686, we have to find the factors of both numbers and list the highest common factor.

The factors of 1683 are 1, 3, 9, 11, 17, 33, 51, 99, 153, 187, 561, 1683

The factors of 3686 are 1, 2, 19, 38, 97, 194, 1843, 3686

The HCF of 1683,3686 is 1.

Lets's calculate GCF of 1683,3686

Greatest Common Factor (GCF) of 1683,3686 By Common Division

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

Greatest Common Factor of 1683,3686 By Matching Biggest Common Factor Method

Now, list down the factors of 1683

1,3,9,11,17,33,51,99,153,187,561,1683

Now, list down the factors of 3686

1,2,19,38,97,194,1843,3686

Greatest Common Factor

We found the factors 1683,3686 . The biggest common factor number is the GCF number.
So the greatest common factor 1683,3686 is 1.

Lets's calculate LCM of 676,5964

Lowest Common Multiple of 676,5964 using Common Division

2	676, 5964
2	338, 2982
	169, 1491

∴ So the LCM of the given numbers is 2 x 2 x 169 x 1491 = 1007916

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1007916

Therefore, the GCF of Fractions 1683/676,3686/5964 is 1/1007916

Least Common Multiple of 676,5964 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 676,5964 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(676,5964) = 4

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

GCF(676,5964) x common factors =4 x 1 = 4

LCM(676,5964) = ( 676 × 5964 ) / 4

LCM(676,5964) = 4031664 / 4

LCM(676,5964) = 1007916

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FAQs on GCF of Fractions of 1683/676, 3686/5964

1. What is the HCF of 1683,3686?

The HCF of 1683,3686 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 1683/676, 3686/5964?

Answer: GCF of Numerators as per given numbers 1683/676, 3686/5964 is

GCF of Numerators i.e. for 1683,3686 is 1

LCM of denominators i.e. for 676,5964 is 1007916.

Thus, GCF of Fractions is 1/1007916.Finally, GCF of Fractions for 1683/676, 3686/5964 is 1/1007916.