How to Find GCF of 800/362, 770/506?

GCF of 800/362, 770/506

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 800/362, 770/506 i.e 10/91586 easily. The following is the detailed procedure to determine the greatest common factor of fractions 800/362, 770/506.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 800/362,770/506?

Given fractions are 800/362,770/506

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 800/362,770/506, numerators are 800,770

Denominators are 362,506

The GCF of 800,770 is 10 .

LCM of 362,506 is 91586.

The greatest common factor of 800/362,770/506 = [GCF of 800,770]/[LCM of 362,506]= 10/91586

Therefore, the GCF of 800/362,770/506 is 10/91586.

Greatest Common Factor of 800,770

To find the highest common factor of 800,770, we have to find the factors of both numbers and list the highest common factor.

The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800

The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770

The HCF of 800,770 is 10.

Lets's calculate GCF of 800,770

Greatest Common Factor (GCF) of 800,770 By Common Division

2	800, 770
5	400, 385
	80, 77

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 800,770 By Matching Biggest Common Factor Method

Now, list down the factors of 800

1,2,4,5,8,10,16,20,25,32,40,50,80,100,160,200,400,800

Now, list down the factors of 770

1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770

Greatest Common Factor

We found the factors 800,770 . The biggest common factor number is the GCF number.
So the greatest common factor 800,770 is 10.

Lets's calculate LCM of 362,506

Lowest Common Multiple of 362,506 using Common Division

2	362, 506
	181, 253

∴ So the LCM of the given numbers is 2 x 181 x 253 = 91586

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/91586

Therefore, the GCF of Fractions 800/362,770/506 is 10/91586

Least Common Multiple of 362,506 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 362,506 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(362,506) = 2

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

GCF(362,506) x common factors =2 x 1 = 2

LCM(362,506) = ( 362 × 506 ) / 2

LCM(362,506) = 183172 / 2

LCM(362,506) = 91586

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FAQs on GCF of Fractions of 800/362, 770/506

1. What is the HCF of 800,770?

The HCF of 800,770 is 10

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 800/362, 770/506?

Answer: GCF of Numerators as per given numbers 800/362, 770/506 is

GCF of Numerators i.e. for 800,770 is 10

LCM of denominators i.e. for 362,506 is 91586.

Thus, GCF of Fractions is 10/91586.Finally, GCF of Fractions for 800/362, 770/506 is 10/91586.