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GCF of 812/977, 749/997

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 812/977, 749/997 i.e 7/974069 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/977, 749/997.

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 812/977,749/997?

Given fractions are 812/977,749/997

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 812/977,749/997, numerators are 812,749

Denominators are 977,997

The GCF of 812,749 is 7 .

LCM of 977,997 is 974069.

The greatest common factor of 812/977,749/997 = [GCF of 812,749]/[LCM of 977,997]= 7/974069

Therefore, the GCF of 812/977,749/997 is 7/974069.

Greatest Common Factor of 812,749

To find the highest common factor of 812,749, 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 749 are 1, 7, 107, 749

The HCF of 812,749 is 7.

Lets's calculate GCF of 812,749

Greatest Common Factor (GCF) of 812,749 By Common Division

7 812, 749
116, 107

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 812,749 By Matching Biggest Common Factor Method

Greatest Common Factor of 812,749 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 749

:

1,7,107,749

Greatest Common Factor

We found the factors 812,749 . The biggest common factor number is the GCF number.
So the greatest common factor 812,749 is 7.

Lets's calculate LCM of 977,997

Lowest Common Multiple of 977,997 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 974069

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/974069

Therefore, the GCF of Fractions 812/977,749/997 is 7/974069

Least Common Multiple of 977,997 with GCF Formula

Least Common Multiple of 977,997 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 977,997 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(977,997) = 1

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

GCF(977,997) x common factors =1 x 1 = 1

LCM(977,997) = ( 977 × 997 ) / 1

LCM(977,997) = 974069 / 1

LCM(977,997) = 974069


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FAQs on GCF of Fractions of 812/977, 749/997

1. What is the HCF of 812,749?

The HCF of 812,749 is 7

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 812/977, 749/997?

Answer: GCF of Numerators as per given numbers 812/977, 749/997 is

GCF of Numerators i.e. for 812,749 is 7

LCM of denominators i.e. for 977,997 is 974069.

Thus, GCF of Fractions is 7/974069.Finally, GCF of Fractions for 812/977, 749/997 is 7/974069.