How to Find GCF of 17/125, 31/639, 689/672?

GCF of 17/125, 31/639, 689/672

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 17/125, 31/639, 689/672 i.e 1/17892000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/125, 31/639, 689/672.

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 17/125,31/639,689/672?

Given fractions are 17/125,31/639,689/672

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 17/125,31/639,689/672, numerators are 17,31,689

Denominators are 125,639,672

The GCF of 17,31,689 is 1 .

LCM of 125,639,672 is 17892000.

The greatest common factor of 17/125,31/639,689/672 = [GCF of 17,31,689]/[LCM of 125,639,672]= 1/17892000

Therefore, the GCF of 17/125,31/639,689/672 is 1/17892000.

Greatest Common Factor of 17,31,689

To find the highest common factor of 17,31,689, we have to find the factors of both numbers and list the highest common factor.

The factors of 17 are 1, 17

The factors of 31 are 1, 31

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

The HCF of 17,31,689 is 1.

Lets's calculate GCF of 17,31,689

Greatest Common Factor (GCF) of 17,31,689 By Common Division

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

Greatest Common Factor of 17,31,689 By Matching Biggest Common Factor Method

Now, list down the factors of 17

1,17

Now, list down the factors of 31

1,31

Now, list down the factors of 689

1,13,53,689

Greatest Common Factor

We found the factors 17,31,689 . The biggest common factor number is the GCF number.
So the greatest common factor 17,31,689 is 1.

Lets's calculate LCM of 125,639,672

Lowest Common Multiple of 125,639,672 using Common Division

3	125, 639, 672
	125, 213, 224

∴ So the LCM of the given numbers is 3 x 125 x 213 x 224 = 17892000

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17892000

Therefore, the GCF of Fractions 17/125,31/639,689/672 is 1/17892000

Least Common Multiple of 125,639,672 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 125,639,672 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(125,639,672) = 1

common factors(in case of two or more numbers have common factors) = 3

GCF(125,639,672) x common factors =1 x 3 = 3

LCM(125,639,672) = ( 125 × 639 × 672 ) / 3

LCM(125,639,672) = 53676000 / 3

LCM(125,639,672) = 17892000

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 17/125, 31/639, 689/672

1. What is the HCF of 17,31,689?

The HCF of 17,31,689 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 17/125, 31/639, 689/672?

Answer: GCF of Numerators as per given numbers 17/125, 31/639, 689/672 is

GCF of Numerators i.e. for 17,31,689 is 1

LCM of denominators i.e. for 125,639,672 is 17892000.

Thus, GCF of Fractions is 1/17892000.Finally, GCF of Fractions for 17/125, 31/639, 689/672 is 1/17892000.