How to Find GCF of 769/610, 828/142?

GCF of 769/610, 828/142

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 769/610, 828/142 i.e 1/43310 easily. The following is the detailed procedure to determine the greatest common factor of fractions 769/610, 828/142.

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 769/610,828/142?

Given fractions are 769/610,828/142

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 769/610,828/142, numerators are 769,828

Denominators are 610,142

The GCF of 769,828 is 1 .

LCM of 610,142 is 43310.

The greatest common factor of 769/610,828/142 = [GCF of 769,828]/[LCM of 610,142]= 1/43310

Therefore, the GCF of 769/610,828/142 is 1/43310.

Greatest Common Factor of 769,828

To find the highest common factor of 769,828, we have to find the factors of both numbers and list the highest common factor.

The factors of 769 are 1, 769

The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828

The HCF of 769,828 is 1.

Lets's calculate GCF of 769,828

Greatest Common Factor (GCF) of 769,828 By Common Division

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

Greatest Common Factor of 769,828 By Matching Biggest Common Factor Method

Now, list down the factors of 769

1,769

Now, list down the factors of 828

1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828

Greatest Common Factor

We found the factors 769,828 . The biggest common factor number is the GCF number.
So the greatest common factor 769,828 is 1.

Lets's calculate LCM of 610,142

Lowest Common Multiple of 610,142 using Common Division

2	610, 142
	305, 71

∴ So the LCM of the given numbers is 2 x 305 x 71 = 43310

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43310

Therefore, the GCF of Fractions 769/610,828/142 is 1/43310

Least Common Multiple of 610,142 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 610,142 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(610,142) = 2

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

GCF(610,142) x common factors =2 x 1 = 2

LCM(610,142) = ( 610 × 142 ) / 2

LCM(610,142) = 86620 / 2

LCM(610,142) = 43310

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FAQs on GCF of Fractions of 769/610, 828/142

1. What is the HCF of 769,828?

The HCF of 769,828 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 769/610, 828/142?

Answer: GCF of Numerators as per given numbers 769/610, 828/142 is

GCF of Numerators i.e. for 769,828 is 1

LCM of denominators i.e. for 610,142 is 43310.

Thus, GCF of Fractions is 1/43310.Finally, GCF of Fractions for 769/610, 828/142 is 1/43310.