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GCF of 812/39, 574/967

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 812/39, 574/967 i.e 14/37713 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/39, 574/967.

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 812/39,574/967?

Given fractions are 812/39,574/967

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 812/39,574/967, numerators are 812,574

Denominators are 39,967

The GCF of 812,574 is 14 .

LCM of 39,967 is 37713.

The greatest common factor of 812/39,574/967 = [GCF of 812,574]/[LCM of 39,967]= 14/37713

Therefore, the GCF of 812/39,574/967 is 14/37713.

Greatest Common Factor of 812,574

To find the highest common factor of 812,574, we have to find the factors of both numbers and list the highest common factor.

The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812

The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574

The HCF of 812,574 is 14.

Lets's calculate GCF of 812,574

Greatest Common Factor (GCF) of 812,574 By Common Division

2 812, 574
7 406, 287
58, 41

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 812,574 By Matching Biggest Common Factor Method

Greatest Common Factor of 812,574 By Matching Biggest Common Factor Method

Now, list down the factors of 812

:

1,2,4,7,14,28,29,58,116,203,406,812

Now, list down the factors of 574

:

1,2,7,14,41,82,287,574

Greatest Common Factor

We found the factors 812,574 . The biggest common factor number is the GCF number.
So the greatest common factor 812,574 is 14.


Lets's calculate LCM of 39,967

Lowest Common Multiple of 39,967 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 37713

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/37713

Therefore, the GCF of Fractions 812/39,574/967 is 14/37713

Least Common Multiple of 39,967 with GCF Formula

Least Common Multiple of 39,967 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 39,967 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(39,967) = 1

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

GCF(39,967) x common factors =1 x 1 = 1

LCM(39,967) = ( 39 × 967 ) / 1

LCM(39,967) = 37713 / 1

LCM(39,967) = 37713


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 812/39, 574/967

1. What is the HCF of 812,574?

The HCF of 812,574 is 14

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 812/39, 574/967?

Answer: GCF of Numerators as per given numbers 812/39, 574/967 is

GCF of Numerators i.e. for 812,574 is 14

LCM of denominators i.e. for 39,967 is 37713.

Thus, GCF of Fractions is 14/37713.Finally, GCF of Fractions for 812/39, 574/967 is 14/37713.