How to Find GCF of 6977/172, 3914/596?

GCF of 6977/172, 3914/596

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 6977/172, 3914/596 i.e 1/25628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6977/172, 3914/596.

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 6977/172,3914/596?

Given fractions are 6977/172,3914/596

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 6977/172,3914/596, numerators are 6977,3914

Denominators are 172,596

The GCF of 6977,3914 is 1 .

LCM of 172,596 is 25628.

The greatest common factor of 6977/172,3914/596 = [GCF of 6977,3914]/[LCM of 172,596]= 1/25628

Therefore, the GCF of 6977/172,3914/596 is 1/25628.

Greatest Common Factor of 6977,3914

To find the highest common factor of 6977,3914, we have to find the factors of both numbers and list the highest common factor.

The factors of 6977 are 1, 6977

The factors of 3914 are 1, 2, 19, 38, 103, 206, 1957, 3914

The HCF of 6977,3914 is 1.

Lets's calculate GCF of 6977,3914

Greatest Common Factor (GCF) of 6977,3914 By Common Division

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

Greatest Common Factor of 6977,3914 By Matching Biggest Common Factor Method

Now, list down the factors of 6977

1,6977

Now, list down the factors of 3914

1,2,19,38,103,206,1957,3914

Greatest Common Factor

We found the factors 6977,3914 . The biggest common factor number is the GCF number.
So the greatest common factor 6977,3914 is 1.

Lets's calculate LCM of 172,596

Lowest Common Multiple of 172,596 using Common Division

2	172, 596
2	86, 298
	43, 149

∴ So the LCM of the given numbers is 2 x 2 x 43 x 149 = 25628

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25628

Therefore, the GCF of Fractions 6977/172,3914/596 is 1/25628

Least Common Multiple of 172,596 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 172,596 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(172,596) = 4

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

GCF(172,596) x common factors =4 x 1 = 4

LCM(172,596) = ( 172 × 596 ) / 4

LCM(172,596) = 102512 / 4

LCM(172,596) = 25628

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FAQs on GCF of Fractions of 6977/172, 3914/596

1. What is the HCF of 6977,3914?

The HCF of 6977,3914 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 6977/172, 3914/596?

Answer: GCF of Numerators as per given numbers 6977/172, 3914/596 is

GCF of Numerators i.e. for 6977,3914 is 1

LCM of denominators i.e. for 172,596 is 25628.

Thus, GCF of Fractions is 1/25628.Finally, GCF of Fractions for 6977/172, 3914/596 is 1/25628.