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GCF of 114/16, 919/400

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 114/16, 919/400 i.e 1/400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 114/16, 919/400.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 114/16,919/400?

Given fractions are 114/16,919/400

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 114/16,919/400, numerators are 114,919

Denominators are 16,400

The GCF of 114,919 is 1 .

LCM of 16,400 is 400.

The greatest common factor of 114/16,919/400 = [GCF of 114,919]/[LCM of 16,400]= 1/400

Therefore, the GCF of 114/16,919/400 is 1/400.

Greatest Common Factor of 114,919

To find the highest common factor of 114,919, we have to find the factors of both numbers and list the highest common factor.

The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114

The factors of 919 are 1, 919

The HCF of 114,919 is 1.

Lets's calculate GCF of 114,919

Greatest Common Factor (GCF) of 114,919 By Common Division

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

Greatest Common Factor of 114,919 By Matching Biggest Common Factor Method

Greatest Common Factor of 114,919 By Matching Biggest Common Factor Method

Now, list down the factors of 114

:

1,2,3,6,19,38,57,114

Now, list down the factors of 919

:

1,919

Greatest Common Factor

We found the factors 114,919 . The biggest common factor number is the GCF number.
So the greatest common factor 114,919 is 1.

Lets's calculate LCM of 16,400

Lowest Common Multiple of 16,400 using Common Division

2 16, 400
2 8, 200
2 4, 100
2 2, 50
1, 25

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 1 x 25 = 400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/400

Therefore, the GCF of Fractions 114/16,919/400 is 1/400

Least Common Multiple of 16,400 with GCF Formula

Least Common Multiple of 16,400 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 16,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,400) = 16

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

GCF(16,400) x common factors =16 x 1 = 16

LCM(16,400) = ( 16 × 400 ) / 16

LCM(16,400) = 6400 / 16

LCM(16,400) = 400


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FAQs on GCF of Fractions of 114/16, 919/400

1. What is the HCF of 114,919?

The HCF of 114,919 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 114/16, 919/400?

Answer: GCF of Numerators as per given numbers 114/16, 919/400 is

GCF of Numerators i.e. for 114,919 is 1

LCM of denominators i.e. for 16,400 is 400.

Thus, GCF of Fractions is 1/400.Finally, GCF of Fractions for 114/16, 919/400 is 1/400.