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GCF of 706/31, 976/3805

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 706/31, 976/3805 i.e 2/117955 easily. The following is the detailed procedure to determine the greatest common factor of fractions 706/31, 976/3805.

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 706/31,976/3805?

Given fractions are 706/31,976/3805

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 706/31,976/3805, numerators are 706,976

Denominators are 31,3805

The GCF of 706,976 is 2 .

LCM of 31,3805 is 117955.

The greatest common factor of 706/31,976/3805 = [GCF of 706,976]/[LCM of 31,3805]= 2/117955

Therefore, the GCF of 706/31,976/3805 is 2/117955.

Greatest Common Factor of 706,976

To find the highest common factor of 706,976, we have to find the factors of both numbers and list the highest common factor.

The factors of 706 are 1, 2, 353, 706

The factors of 976 are 1, 2, 4, 8, 16, 61, 122, 244, 488, 976

The HCF of 706,976 is 2.

Lets's calculate GCF of 706,976

Greatest Common Factor (GCF) of 706,976 By Common Division

2 706, 976
353, 488

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

Greatest Common Factor of 706,976 By Matching Biggest Common Factor Method

Greatest Common Factor of 706,976 By Matching Biggest Common Factor Method

Now, list down the factors of 706

:

1,2,353,706

Now, list down the factors of 976

:

1,2,4,8,16,61,122,244,488,976

Greatest Common Factor

We found the factors 706,976 . The biggest common factor number is the GCF number.
So the greatest common factor 706,976 is 2.

Lets's calculate LCM of 31,3805

Lowest Common Multiple of 31,3805 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 117955

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/117955

Therefore, the GCF of Fractions 706/31,976/3805 is 2/117955

Least Common Multiple of 31,3805 with GCF Formula

Least Common Multiple of 31,3805 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 31,3805 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,3805) = 1

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

GCF(31,3805) x common factors =1 x 1 = 1

LCM(31,3805) = ( 31 × 3805 ) / 1

LCM(31,3805) = 117955 / 1

LCM(31,3805) = 117955


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FAQs on GCF of Fractions of 706/31, 976/3805

1. What is the HCF of 706,976?

The HCF of 706,976 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 706/31, 976/3805?

Answer: GCF of Numerators as per given numbers 706/31, 976/3805 is

GCF of Numerators i.e. for 706,976 is 2

LCM of denominators i.e. for 31,3805 is 117955.

Thus, GCF of Fractions is 2/117955.Finally, GCF of Fractions for 706/31, 976/3805 is 2/117955.