How to Find GCF of 509/284, 4862/700?

GCF of 509/284, 4862/700

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 509/284, 4862/700 i.e 1/49700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 509/284, 4862/700.

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 509/284,4862/700?

Given fractions are 509/284,4862/700

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 509/284,4862/700, numerators are 509,4862

Denominators are 284,700

The GCF of 509,4862 is 1 .

LCM of 284,700 is 49700.

The greatest common factor of 509/284,4862/700 = [GCF of 509,4862]/[LCM of 284,700]= 1/49700

Therefore, the GCF of 509/284,4862/700 is 1/49700.

Greatest Common Factor of 509,4862

To find the highest common factor of 509,4862, we have to find the factors of both numbers and list the highest common factor.

The factors of 509 are 1, 509

The factors of 4862 are 1, 2, 11, 13, 17, 22, 26, 34, 143, 187, 221, 286, 374, 442, 2431, 4862

The HCF of 509,4862 is 1.

Lets's calculate GCF of 509,4862

Greatest Common Factor (GCF) of 509,4862 By Common Division

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

Greatest Common Factor of 509,4862 By Matching Biggest Common Factor Method

Now, list down the factors of 509

1,509

Now, list down the factors of 4862

1,2,11,13,17,22,26,34,143,187,221,286,374,442,2431,4862

Greatest Common Factor

We found the factors 509,4862 . The biggest common factor number is the GCF number.
So the greatest common factor 509,4862 is 1.

Lets's calculate LCM of 284,700

Lowest Common Multiple of 284,700 using Common Division

2	284, 700
2	142, 350
	71, 175

∴ So the LCM of the given numbers is 2 x 2 x 71 x 175 = 49700

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/49700

Therefore, the GCF of Fractions 509/284,4862/700 is 1/49700

Least Common Multiple of 284,700 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 284,700 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(284,700) = 4

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

GCF(284,700) x common factors =4 x 1 = 4

LCM(284,700) = ( 284 × 700 ) / 4

LCM(284,700) = 198800 / 4

LCM(284,700) = 49700

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FAQs on GCF of Fractions of 509/284, 4862/700

1. What is the HCF of 509,4862?

The HCF of 509,4862 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 509/284, 4862/700?

Answer: GCF of Numerators as per given numbers 509/284, 4862/700 is

GCF of Numerators i.e. for 509,4862 is 1

LCM of denominators i.e. for 284,700 is 49700.

Thus, GCF of Fractions is 1/49700.Finally, GCF of Fractions for 509/284, 4862/700 is 1/49700.