How to Find GCF of 1709/752, 3442/5372?

GCF of 1709/752, 3442/5372

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 1709/752, 3442/5372 i.e 1/1009936 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1709/752, 3442/5372.

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 1709/752,3442/5372?

Given fractions are 1709/752,3442/5372

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 1709/752,3442/5372, numerators are 1709,3442

Denominators are 752,5372

The GCF of 1709,3442 is 1 .

LCM of 752,5372 is 1009936.

The greatest common factor of 1709/752,3442/5372 = [GCF of 1709,3442]/[LCM of 752,5372]= 1/1009936

Therefore, the GCF of 1709/752,3442/5372 is 1/1009936.

Greatest Common Factor of 1709,3442

To find the highest common factor of 1709,3442, we have to find the factors of both numbers and list the highest common factor.

The factors of 1709 are 1, 1709

The factors of 3442 are 1, 2, 1721, 3442

The HCF of 1709,3442 is 1.

Lets's calculate GCF of 1709,3442

Greatest Common Factor (GCF) of 1709,3442 By Common Division

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

Greatest Common Factor of 1709,3442 By Matching Biggest Common Factor Method

Now, list down the factors of 1709

1,1709

Now, list down the factors of 3442

1,2,1721,3442

Greatest Common Factor

We found the factors 1709,3442 . The biggest common factor number is the GCF number.
So the greatest common factor 1709,3442 is 1.

Lets's calculate LCM of 752,5372

Lowest Common Multiple of 752,5372 using Common Division

2	752, 5372
2	376, 2686
	188, 1343

∴ So the LCM of the given numbers is 2 x 2 x 188 x 1343 = 1009936

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1009936

Therefore, the GCF of Fractions 1709/752,3442/5372 is 1/1009936

Least Common Multiple of 752,5372 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 752,5372 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(752,5372) = 4

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

GCF(752,5372) x common factors =4 x 1 = 4

LCM(752,5372) = ( 752 × 5372 ) / 4

LCM(752,5372) = 4039744 / 4

LCM(752,5372) = 1009936

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FAQs on GCF of Fractions of 1709/752, 3442/5372

1. What is the HCF of 1709,3442?

The HCF of 1709,3442 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 1709/752, 3442/5372?

Answer: GCF of Numerators as per given numbers 1709/752, 3442/5372 is

GCF of Numerators i.e. for 1709,3442 is 1

LCM of denominators i.e. for 752,5372 is 1009936.

Thus, GCF of Fractions is 1/1009936.Finally, GCF of Fractions for 1709/752, 3442/5372 is 1/1009936.