How to Find GCF of 689/166, 6227/454?

GCF of 689/166, 6227/454

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 689/166, 6227/454 i.e 13/37682 easily. The following is the detailed procedure to determine the greatest common factor of fractions 689/166, 6227/454.

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 689/166,6227/454?

Given fractions are 689/166,6227/454

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 689/166,6227/454, numerators are 689,6227

Denominators are 166,454

The GCF of 689,6227 is 13 .

LCM of 166,454 is 37682.

The greatest common factor of 689/166,6227/454 = [GCF of 689,6227]/[LCM of 166,454]= 13/37682

Therefore, the GCF of 689/166,6227/454 is 13/37682.

Greatest Common Factor of 689,6227

To find the highest common factor of 689,6227, we have to find the factors of both numbers and list the highest common factor.

The factors of 689 are 1, 13, 53, 689

The factors of 6227 are 1, 13, 479, 6227

The HCF of 689,6227 is 13.

Lets's calculate GCF of 689,6227

Greatest Common Factor (GCF) of 689,6227 By Common Division

13	689, 6227
	53, 479

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 689,6227 By Matching Biggest Common Factor Method

Now, list down the factors of 689

1,13,53,689

Now, list down the factors of 6227

1,13,479,6227

Greatest Common Factor

We found the factors 689,6227 . The biggest common factor number is the GCF number.
So the greatest common factor 689,6227 is 13.

Lets's calculate LCM of 166,454

Lowest Common Multiple of 166,454 using Common Division

2	166, 454
	83, 227

∴ So the LCM of the given numbers is 2 x 83 x 227 = 37682

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/37682

Therefore, the GCF of Fractions 689/166,6227/454 is 13/37682

Least Common Multiple of 166,454 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 166,454 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(166,454) = 2

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

GCF(166,454) x common factors =2 x 1 = 2

LCM(166,454) = ( 166 × 454 ) / 2

LCM(166,454) = 75364 / 2

LCM(166,454) = 37682

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FAQs on GCF of Fractions of 689/166, 6227/454

1. What is the HCF of 689,6227?

The HCF of 689,6227 is 13

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 689/166, 6227/454?

Answer: GCF of Numerators as per given numbers 689/166, 6227/454 is

GCF of Numerators i.e. for 689,6227 is 13

LCM of denominators i.e. for 166,454 is 37682.

Thus, GCF of Fractions is 13/37682.Finally, GCF of Fractions for 689/166, 6227/454 is 13/37682.