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GCF of 782/356, 506/859

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 782/356, 506/859 i.e 46/305804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 782/356, 506/859.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 782/356,506/859?

Given fractions are 782/356,506/859

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 782/356,506/859, numerators are 782,506

Denominators are 356,859

The GCF of 782,506 is 46 .

LCM of 356,859 is 305804.

The greatest common factor of 782/356,506/859 = [GCF of 782,506]/[LCM of 356,859]= 46/305804

Therefore, the GCF of 782/356,506/859 is 46/305804.

Greatest Common Factor of 782,506

To find the highest common factor of 782,506, we have to find the factors of both numbers and list the highest common factor.

The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782

The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506

The HCF of 782,506 is 46.

Lets's calculate GCF of 782,506

Greatest Common Factor (GCF) of 782,506 By Common Division

2 782, 506
23 391, 253
17, 11

∴ So the GCF of the given numbers is 2 x 23 = 46

Greatest Common Factor of 782,506 By Matching Biggest Common Factor Method

Greatest Common Factor of 782,506 By Matching Biggest Common Factor Method

Now, list down the factors of 782

:

1,2,17,23,34,46,391,782

Now, list down the factors of 506

:

1,2,11,22,23,46,253,506

Greatest Common Factor

We found the factors 782,506 . The biggest common factor number is the GCF number.
So the greatest common factor 782,506 is 46.

Lets's calculate LCM of 356,859

Lowest Common Multiple of 356,859 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 305804

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/305804

Therefore, the GCF of Fractions 782/356,506/859 is 46/305804

Least Common Multiple of 356,859 with GCF Formula

Least Common Multiple of 356,859 with GCF Formula

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

We need to calculate greatest common factor of 356,859 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(356,859) = 1

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

GCF(356,859) x common factors =1 x 1 = 1

LCM(356,859) = ( 356 × 859 ) / 1

LCM(356,859) = 305804 / 1

LCM(356,859) = 305804


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FAQs on GCF of Fractions of 782/356, 506/859

1. What is the HCF of 782,506?

The HCF of 782,506 is 46

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 782/356, 506/859?

Answer: GCF of Numerators as per given numbers 782/356, 506/859 is

GCF of Numerators i.e. for 782,506 is 46

LCM of denominators i.e. for 356,859 is 305804.

Thus, GCF of Fractions is 46/305804.Finally, GCF of Fractions for 782/356, 506/859 is 46/305804.