How to Find GCF of 810/596, 7462/628?

GCF of 810/596, 7462/628

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 810/596, 7462/628 i.e 2/93572 easily. The following is the detailed procedure to determine the greatest common factor of fractions 810/596, 7462/628.

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 810/596,7462/628?

Given fractions are 810/596,7462/628

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 810/596,7462/628, numerators are 810,7462

Denominators are 596,628

The GCF of 810,7462 is 2 .

LCM of 596,628 is 93572.

The greatest common factor of 810/596,7462/628 = [GCF of 810,7462]/[LCM of 596,628]= 2/93572

Therefore, the GCF of 810/596,7462/628 is 2/93572.

Greatest Common Factor of 810,7462

To find the highest common factor of 810,7462, we have to find the factors of both numbers and list the highest common factor.

The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810

The factors of 7462 are 1, 2, 7, 13, 14, 26, 41, 82, 91, 182, 287, 533, 574, 1066, 3731, 7462

The HCF of 810,7462 is 2.

Lets's calculate GCF of 810,7462

Greatest Common Factor (GCF) of 810,7462 By Common Division

2	810, 7462
	405, 3731

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 810,7462 By Matching Biggest Common Factor Method

Now, list down the factors of 810

1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810

Now, list down the factors of 7462

1,2,7,13,14,26,41,82,91,182,287,533,574,1066,3731,7462

Greatest Common Factor

We found the factors 810,7462 . The biggest common factor number is the GCF number.
So the greatest common factor 810,7462 is 2.

Lets's calculate LCM of 596,628

Lowest Common Multiple of 596,628 using Common Division

2	596, 628
2	298, 314
	149, 157

∴ So the LCM of the given numbers is 2 x 2 x 149 x 157 = 93572

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/93572

Therefore, the GCF of Fractions 810/596,7462/628 is 2/93572

Least Common Multiple of 596,628 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 596,628 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(596,628) = 4

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

GCF(596,628) x common factors =4 x 1 = 4

LCM(596,628) = ( 596 × 628 ) / 4

LCM(596,628) = 374288 / 4

LCM(596,628) = 93572

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FAQs on GCF of Fractions of 810/596, 7462/628

1. What is the HCF of 810,7462?

The HCF of 810,7462 is 2

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 810/596, 7462/628?

Answer: GCF of Numerators as per given numbers 810/596, 7462/628 is

GCF of Numerators i.e. for 810,7462 is 2

LCM of denominators i.e. for 596,628 is 93572.

Thus, GCF of Fractions is 2/93572.Finally, GCF of Fractions for 810/596, 7462/628 is 2/93572.