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GCF of 914/76, 206/767

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 914/76, 206/767 i.e 2/58292 easily. The following is the detailed procedure to determine the greatest common factor of fractions 914/76, 206/767.

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 914/76,206/767?

Given fractions are 914/76,206/767

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 914/76,206/767, numerators are 914,206

Denominators are 76,767

The GCF of 914,206 is 2 .

LCM of 76,767 is 58292.

The greatest common factor of 914/76,206/767 = [GCF of 914,206]/[LCM of 76,767]= 2/58292

Therefore, the GCF of 914/76,206/767 is 2/58292.

Greatest Common Factor of 914,206

To find the highest common factor of 914,206, 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 206 are 1, 2, 103, 206

The HCF of 914,206 is 2.

Lets's calculate GCF of 914,206

Greatest Common Factor (GCF) of 914,206 By Common Division

2 914, 206
457, 103

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

Greatest Common Factor of 914,206 By Matching Biggest Common Factor Method

Greatest Common Factor of 914,206 By Matching Biggest Common Factor Method

Now, list down the factors of 914

:

1,2,457,914

Now, list down the factors of 206

:

1,2,103,206

Greatest Common Factor

We found the factors 914,206 . The biggest common factor number is the GCF number.
So the greatest common factor 914,206 is 2.

Lets's calculate LCM of 76,767

Lowest Common Multiple of 76,767 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 58292

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/58292

Therefore, the GCF of Fractions 914/76,206/767 is 2/58292

Least Common Multiple of 76,767 with GCF Formula

Least Common Multiple of 76,767 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 76,767 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,767) = 1

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

GCF(76,767) x common factors =1 x 1 = 1

LCM(76,767) = ( 76 × 767 ) / 1

LCM(76,767) = 58292 / 1

LCM(76,767) = 58292


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FAQs on GCF of Fractions of 914/76, 206/767

1. What is the HCF of 914,206?

The HCF of 914,206 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 914/76, 206/767?

Answer: GCF of Numerators as per given numbers 914/76, 206/767 is

GCF of Numerators i.e. for 914,206 is 2

LCM of denominators i.e. for 76,767 is 58292.

Thus, GCF of Fractions is 2/58292.Finally, GCF of Fractions for 914/76, 206/767 is 2/58292.