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GCF of 870/53, 406/791

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 870/53, 406/791 i.e 58/41923 easily. The following is the detailed procedure to determine the greatest common factor of fractions 870/53, 406/791.

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 870/53,406/791?

Given fractions are 870/53,406/791

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 870/53,406/791, numerators are 870,406

Denominators are 53,791

The GCF of 870,406 is 58 .

LCM of 53,791 is 41923.

The greatest common factor of 870/53,406/791 = [GCF of 870,406]/[LCM of 53,791]= 58/41923

Therefore, the GCF of 870/53,406/791 is 58/41923.

Greatest Common Factor of 870,406

To find the highest common factor of 870,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 870,406 is 58.

Lets's calculate GCF of 870,406

Greatest Common Factor (GCF) of 870,406 By Common Division

2 870, 406
29 435, 203
15, 7

∴ So the GCF of the given numbers is 2 x 29 = 58

Greatest Common Factor of 870,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 870,406 By Matching Biggest Common Factor Method

Now, list down the factors of 870

:

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Now, list down the factors of 406

:

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 870,406 . The biggest common factor number is the GCF number.
So the greatest common factor 870,406 is 58.

Lets's calculate LCM of 53,791

Lowest Common Multiple of 53,791 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 41923

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 58/41923

Therefore, the GCF of Fractions 870/53,406/791 is 58/41923

Least Common Multiple of 53,791 with GCF Formula

Least Common Multiple of 53,791 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 53,791 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(53,791) = 1

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

GCF(53,791) x common factors =1 x 1 = 1

LCM(53,791) = ( 53 × 791 ) / 1

LCM(53,791) = 41923 / 1

LCM(53,791) = 41923


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FAQs on GCF of Fractions of 870/53, 406/791

1. What is the HCF of 870,406?

The HCF of 870,406 is 58

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 870/53, 406/791?

Answer: GCF of Numerators as per given numbers 870/53, 406/791 is

GCF of Numerators i.e. for 870,406 is 58

LCM of denominators i.e. for 53,791 is 41923.

Thus, GCF of Fractions is 58/41923.Finally, GCF of Fractions for 870/53, 406/791 is 58/41923.