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GCF of 914/38, 208/2687

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 914/38, 208/2687 i.e 2/102106 easily. The following is the detailed procedure to determine the greatest common factor of fractions 914/38, 208/2687.

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 914/38,208/2687?

Given fractions are 914/38,208/2687

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 914/38,208/2687, numerators are 914,208

Denominators are 38,2687

The GCF of 914,208 is 2 .

LCM of 38,2687 is 102106.

The greatest common factor of 914/38,208/2687 = [GCF of 914,208]/[LCM of 38,2687]= 2/102106

Therefore, the GCF of 914/38,208/2687 is 2/102106.

Greatest Common Factor of 914,208

To find the highest common factor of 914,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 914 are 1, 2, 457, 914

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 914,208 is 2.

Lets's calculate GCF of 914,208

Greatest Common Factor (GCF) of 914,208 By Common Division

2 914, 208
457, 104

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 914,208 By Matching Biggest Common Factor Method

Greatest Common Factor of 914,208 By Matching Biggest Common Factor Method

Now, list down the factors of 914

:

1,2,457,914

Now, list down the factors of 208

:

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 914,208 . The biggest common factor number is the GCF number.
So the greatest common factor 914,208 is 2.

Lets's calculate LCM of 38,2687

Lowest Common Multiple of 38,2687 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 102106

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/102106

Therefore, the GCF of Fractions 914/38,208/2687 is 2/102106

Least Common Multiple of 38,2687 with GCF Formula

Least Common Multiple of 38,2687 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 38,2687 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(38,2687) = 1

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

GCF(38,2687) x common factors =1 x 1 = 1

LCM(38,2687) = ( 38 × 2687 ) / 1

LCM(38,2687) = 102106 / 1

LCM(38,2687) = 102106


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FAQs on GCF of Fractions of 914/38, 208/2687

1. What is the HCF of 914,208?

The HCF of 914,208 is 2

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 914/38, 208/2687?

Answer: GCF of Numerators as per given numbers 914/38, 208/2687 is

GCF of Numerators i.e. for 914,208 is 2

LCM of denominators i.e. for 38,2687 is 102106.

Thus, GCF of Fractions is 2/102106.Finally, GCF of Fractions for 914/38, 208/2687 is 2/102106.