How to Find GCF of 308/347, 1400/777?

GCF of 308/347, 1400/777

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 308/347, 1400/777 i.e 28/269619 easily. The following is the detailed procedure to determine the greatest common factor of fractions 308/347, 1400/777.

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 308/347,1400/777?

Given fractions are 308/347,1400/777

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 308/347,1400/777, numerators are 308,1400

Denominators are 347,777

The GCF of 308,1400 is 28 .

LCM of 347,777 is 269619.

The greatest common factor of 308/347,1400/777 = [GCF of 308,1400]/[LCM of 347,777]= 28/269619

Therefore, the GCF of 308/347,1400/777 is 28/269619.

Greatest Common Factor of 308,1400

To find the highest common factor of 308,1400, we have to find the factors of both numbers and list the highest common factor.

The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

The factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400

The HCF of 308,1400 is 28.

Lets's calculate GCF of 308,1400

Greatest Common Factor (GCF) of 308,1400 By Common Division

2	308, 1400
2	154, 700
7	77, 350
	11, 50

∴ So the GCF of the given numbers is 2 x 2 x 7 = 28

Greatest Common Factor of 308,1400 By Matching Biggest Common Factor Method

Now, list down the factors of 308

1,2,4,7,11,14,22,28,44,77,154,308

Now, list down the factors of 1400

1,2,4,5,7,8,10,14,20,25,28,35,40,50,56,70,100,140,175,200,280,350,700,1400

Greatest Common Factor

We found the factors 308,1400 . The biggest common factor number is the GCF number.
So the greatest common factor 308,1400 is 28.

Lets's calculate LCM of 347,777

Lowest Common Multiple of 347,777 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 269619

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/269619

Therefore, the GCF of Fractions 308/347,1400/777 is 28/269619

Least Common Multiple of 347,777 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 347,777 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(347,777) = 1

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

GCF(347,777) x common factors =1 x 1 = 1

LCM(347,777) = ( 347 × 777 ) / 1

LCM(347,777) = 269619 / 1

LCM(347,777) = 269619

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FAQs on GCF of Fractions of 308/347, 1400/777

1. What is the HCF of 308,1400?

The HCF of 308,1400 is 28

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 308/347, 1400/777?

Answer: GCF of Numerators as per given numbers 308/347, 1400/777 is

GCF of Numerators i.e. for 308,1400 is 28

LCM of denominators i.e. for 347,777 is 269619.

Thus, GCF of Fractions is 28/269619.Finally, GCF of Fractions for 308/347, 1400/777 is 28/269619.