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GCF of 314/998, 8582/206

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 314/998, 8582/206 i.e 2/102794 easily. The following is the detailed procedure to determine the greatest common factor of fractions 314/998, 8582/206.

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 314/998,8582/206?

Given fractions are 314/998,8582/206

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 314/998,8582/206, numerators are 314,8582

Denominators are 998,206

The GCF of 314,8582 is 2 .

LCM of 998,206 is 102794.

The greatest common factor of 314/998,8582/206 = [GCF of 314,8582]/[LCM of 998,206]= 2/102794

Therefore, the GCF of 314/998,8582/206 is 2/102794.

Greatest Common Factor of 314,8582

To find the highest common factor of 314,8582, we have to find the factors of both numbers and list the highest common factor.

The factors of 314 are 1, 2, 157, 314

The factors of 8582 are 1, 2, 7, 14, 613, 1226, 4291, 8582

The HCF of 314,8582 is 2.

Lets's calculate GCF of 314,8582

Greatest Common Factor (GCF) of 314,8582 By Common Division

2 314, 8582
157, 4291

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

Greatest Common Factor of 314,8582 By Matching Biggest Common Factor Method

Greatest Common Factor of 314,8582 By Matching Biggest Common Factor Method

Now, list down the factors of 314

:

1,2,157,314

Now, list down the factors of 8582

:

1,2,7,14,613,1226,4291,8582

Greatest Common Factor

We found the factors 314,8582 . The biggest common factor number is the GCF number.
So the greatest common factor 314,8582 is 2.

Lets's calculate LCM of 998,206

Lowest Common Multiple of 998,206 using Common Division

2 998, 206
499, 103

∴ So the LCM of the given numbers is 2 x 499 x 103 = 102794

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/102794

Therefore, the GCF of Fractions 314/998,8582/206 is 2/102794

Least Common Multiple of 998,206 with GCF Formula

Least Common Multiple of 998,206 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 998,206 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(998,206) = 2

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

GCF(998,206) x common factors =2 x 1 = 2

LCM(998,206) = ( 998 × 206 ) / 2

LCM(998,206) = 205588 / 2

LCM(998,206) = 102794


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FAQs on GCF of Fractions of 314/998, 8582/206

1. What is the HCF of 314,8582?

The HCF of 314,8582 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 314/998, 8582/206?

Answer: GCF of Numerators as per given numbers 314/998, 8582/206 is

GCF of Numerators i.e. for 314,8582 is 2

LCM of denominators i.e. for 998,206 is 102794.

Thus, GCF of Fractions is 2/102794.Finally, GCF of Fractions for 314/998, 8582/206 is 2/102794.