How to Find GCF of 3179/320, 7769/3704?

GCF of 3179/320, 7769/3704

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 3179/320, 7769/3704 i.e 17/148160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3179/320, 7769/3704.

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 3179/320,7769/3704?

Given fractions are 3179/320,7769/3704

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 3179/320,7769/3704, numerators are 3179,7769

Denominators are 320,3704

The GCF of 3179,7769 is 17 .

LCM of 320,3704 is 148160.

The greatest common factor of 3179/320,7769/3704 = [GCF of 3179,7769]/[LCM of 320,3704]= 17/148160

Therefore, the GCF of 3179/320,7769/3704 is 17/148160.

Greatest Common Factor of 3179,7769

To find the highest common factor of 3179,7769, we have to find the factors of both numbers and list the highest common factor.

The factors of 3179 are 1, 11, 17, 187, 289, 3179

The factors of 7769 are 1, 17, 457, 7769

The HCF of 3179,7769 is 17.

Lets's calculate GCF of 3179,7769

Greatest Common Factor (GCF) of 3179,7769 By Common Division

17	3179, 7769
	187, 457

∴ So the GCF of the given numbers is 17 = 17

Greatest Common Factor of 3179,7769 By Matching Biggest Common Factor Method

Now, list down the factors of 3179

1,11,17,187,289,3179

Now, list down the factors of 7769

1,17,457,7769

Greatest Common Factor

We found the factors 3179,7769 . The biggest common factor number is the GCF number.
So the greatest common factor 3179,7769 is 17.

Lets's calculate LCM of 320,3704

Lowest Common Multiple of 320,3704 using Common Division

2	320, 3704
2	160, 1852
2	80, 926
	40, 463

∴ So the LCM of the given numbers is 2 x 2 x 2 x 40 x 463 = 148160

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/148160

Therefore, the GCF of Fractions 3179/320,7769/3704 is 17/148160

Least Common Multiple of 320,3704 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 320,3704 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(320,3704) = 8

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

GCF(320,3704) x common factors =8 x 1 = 8

LCM(320,3704) = ( 320 × 3704 ) / 8

LCM(320,3704) = 1185280 / 8

LCM(320,3704) = 148160

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FAQs on GCF of Fractions of 3179/320, 7769/3704

1. What is the HCF of 3179,7769?

The HCF of 3179,7769 is 17

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 3179/320, 7769/3704?

Answer: GCF of Numerators as per given numbers 3179/320, 7769/3704 is

GCF of Numerators i.e. for 3179,7769 is 17

LCM of denominators i.e. for 320,3704 is 148160.

Thus, GCF of Fractions is 17/148160.Finally, GCF of Fractions for 3179/320, 7769/3704 is 17/148160.