How to Find GCF of 9450/274, 1877/256?

GCF of 9450/274, 1877/256

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 9450/274, 1877/256 i.e 1/35072 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9450/274, 1877/256.

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 9450/274,1877/256?

Given fractions are 9450/274,1877/256

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 9450/274,1877/256, numerators are 9450,1877

Denominators are 274,256

The GCF of 9450,1877 is 1 .

LCM of 274,256 is 35072.

The greatest common factor of 9450/274,1877/256 = [GCF of 9450,1877]/[LCM of 274,256]= 1/35072

Therefore, the GCF of 9450/274,1877/256 is 1/35072.

Greatest Common Factor of 9450,1877

To find the highest common factor of 9450,1877, we have to find the factors of both numbers and list the highest common factor.

The factors of 9450 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 25, 27, 30, 35, 42, 45, 50, 54, 63, 70, 75, 90, 105, 126, 135, 150, 175, 189, 210, 225, 270, 315, 350, 378, 450, 525, 630, 675, 945, 1050, 1350, 1575, 1890, 3150, 4725, 9450

The factors of 1877 are 1, 1877

The HCF of 9450,1877 is 1.

Lets's calculate GCF of 9450,1877

Greatest Common Factor (GCF) of 9450,1877 By Common Division

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

Greatest Common Factor of 9450,1877 By Matching Biggest Common Factor Method

Now, list down the factors of 9450

1,2,3,5,6,7,9,10,14,15,18,21,25,27,30,35,42,45,50,54,63,70,75,90,105,126,135,150,175,189,210,225,270,315,350,378,450,525,630,675,945,1050,1350,1575,1890,3150,4725,9450

Now, list down the factors of 1877

1,1877

Greatest Common Factor

We found the factors 9450,1877 . The biggest common factor number is the GCF number.
So the greatest common factor 9450,1877 is 1.

Lets's calculate LCM of 274,256

Lowest Common Multiple of 274,256 using Common Division

2	274, 256
	137, 128

∴ So the LCM of the given numbers is 2 x 137 x 128 = 35072

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/35072

Therefore, the GCF of Fractions 9450/274,1877/256 is 1/35072

Least Common Multiple of 274,256 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 274,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(274,256) = 2

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

GCF(274,256) x common factors =2 x 1 = 2

LCM(274,256) = ( 274 × 256 ) / 2

LCM(274,256) = 70144 / 2

LCM(274,256) = 35072

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FAQs on GCF of Fractions of 9450/274, 1877/256

1. What is the HCF of 9450,1877?

The HCF of 9450,1877 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 9450/274, 1877/256?

Answer: GCF of Numerators as per given numbers 9450/274, 1877/256 is

GCF of Numerators i.e. for 9450,1877 is 1

LCM of denominators i.e. for 274,256 is 35072.

Thus, GCF of Fractions is 1/35072.Finally, GCF of Fractions for 9450/274, 1877/256 is 1/35072.