How to Find GCF of 830/292, 870/706?

GCF of 830/292, 870/706

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 830/292, 870/706 i.e 10/103076 easily. The following is the detailed procedure to determine the greatest common factor of fractions 830/292, 870/706.

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 830/292,870/706?

Given fractions are 830/292,870/706

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 830/292,870/706, numerators are 830,870

Denominators are 292,706

The GCF of 830,870 is 10 .

LCM of 292,706 is 103076.

The greatest common factor of 830/292,870/706 = [GCF of 830,870]/[LCM of 292,706]= 10/103076

Therefore, the GCF of 830/292,870/706 is 10/103076.

Greatest Common Factor of 830,870

To find the highest common factor of 830,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830

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

The HCF of 830,870 is 10.

Lets's calculate GCF of 830,870

Greatest Common Factor (GCF) of 830,870 By Common Division

2	830, 870
5	415, 435
	83, 87

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 830,870 By Matching Biggest Common Factor Method

Now, list down the factors of 830

1,2,5,10,83,166,415,830

Now, list down the factors of 870

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

Greatest Common Factor

We found the factors 830,870 . The biggest common factor number is the GCF number.
So the greatest common factor 830,870 is 10.

Lets's calculate LCM of 292,706

Lowest Common Multiple of 292,706 using Common Division

2	292, 706
	146, 353

∴ So the LCM of the given numbers is 2 x 146 x 353 = 103076

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/103076

Therefore, the GCF of Fractions 830/292,870/706 is 10/103076

Least Common Multiple of 292,706 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 292,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(292,706) = 2

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

GCF(292,706) x common factors =2 x 1 = 2

LCM(292,706) = ( 292 × 706 ) / 2

LCM(292,706) = 206152 / 2

LCM(292,706) = 103076

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FAQs on GCF of Fractions of 830/292, 870/706

1. What is the HCF of 830,870?

The HCF of 830,870 is 10

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 830/292, 870/706?

Answer: GCF of Numerators as per given numbers 830/292, 870/706 is

GCF of Numerators i.e. for 830,870 is 10

LCM of denominators i.e. for 292,706 is 103076.

Thus, GCF of Fractions is 10/103076.Finally, GCF of Fractions for 830/292, 870/706 is 10/103076.