How to Find GCF of 784/789, 499/206?

GCF of 784/789, 499/206

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 784/789, 499/206 i.e 1/162534 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/789, 499/206.

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 784/789,499/206?

Given fractions are 784/789,499/206

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 784/789,499/206, numerators are 784,499

Denominators are 789,206

The GCF of 784,499 is 1 .

LCM of 789,206 is 162534.

The greatest common factor of 784/789,499/206 = [GCF of 784,499]/[LCM of 789,206]= 1/162534

Therefore, the GCF of 784/789,499/206 is 1/162534.

Greatest Common Factor of 784,499

To find the highest common factor of 784,499, we have to find the factors of both numbers and list the highest common factor.

The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784

The factors of 499 are 1, 499

The HCF of 784,499 is 1.

Lets's calculate GCF of 784,499

Greatest Common Factor (GCF) of 784,499 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 784,499 By Matching Biggest Common Factor Method

Now, list down the factors of 784

1,2,4,7,8,14,16,28,49,56,98,112,196,392,784

Now, list down the factors of 499

1,499

Greatest Common Factor

We found the factors 784,499 . The biggest common factor number is the GCF number.
So the greatest common factor 784,499 is 1.

Lets's calculate LCM of 789,206

Lowest Common Multiple of 789,206 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 162534

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/162534

Therefore, the GCF of Fractions 784/789,499/206 is 1/162534

Least Common Multiple of 789,206 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 789,206 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(789,206) = 1

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

GCF(789,206) x common factors =1 x 1 = 1

LCM(789,206) = ( 789 × 206 ) / 1

LCM(789,206) = 162534 / 1

LCM(789,206) = 162534

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FAQs on GCF of Fractions of 784/789, 499/206

1. What is the HCF of 784,499?

The HCF of 784,499 is 1

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 784/789, 499/206?

Answer: GCF of Numerators as per given numbers 784/789, 499/206 is

GCF of Numerators i.e. for 784,499 is 1

LCM of denominators i.e. for 789,206 is 162534.

Thus, GCF of Fractions is 1/162534.Finally, GCF of Fractions for 784/789, 499/206 is 1/162534.