How to Find GCF of 840/827, 906/778?

GCF of 840/827, 906/778

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 840/827, 906/778 i.e 6/643406 easily. The following is the detailed procedure to determine the greatest common factor of fractions 840/827, 906/778.

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 840/827,906/778?

Given fractions are 840/827,906/778

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 840/827,906/778, numerators are 840,906

Denominators are 827,778

The GCF of 840,906 is 6 .

LCM of 827,778 is 643406.

The greatest common factor of 840/827,906/778 = [GCF of 840,906]/[LCM of 827,778]= 6/643406

Therefore, the GCF of 840/827,906/778 is 6/643406.

Greatest Common Factor of 840,906

To find the highest common factor of 840,906, we have to find the factors of both numbers and list the highest common factor.

The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840

The factors of 906 are 1, 2, 3, 6, 151, 302, 453, 906

The HCF of 840,906 is 6.

Lets's calculate GCF of 840,906

Greatest Common Factor (GCF) of 840,906 By Common Division

2	840, 906
3	420, 453
	140, 151

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 840,906 By Matching Biggest Common Factor Method

Now, list down the factors of 840

1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840

Now, list down the factors of 906

1,2,3,6,151,302,453,906

Greatest Common Factor

We found the factors 840,906 . The biggest common factor number is the GCF number.
So the greatest common factor 840,906 is 6.

Lets's calculate LCM of 827,778

Lowest Common Multiple of 827,778 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 643406

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/643406

Therefore, the GCF of Fractions 840/827,906/778 is 6/643406

Least Common Multiple of 827,778 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 827,778 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(827,778) = 1

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

GCF(827,778) x common factors =1 x 1 = 1

LCM(827,778) = ( 827 × 778 ) / 1

LCM(827,778) = 643406 / 1

LCM(827,778) = 643406

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 840/827, 906/778

1. What is the HCF of 840,906?

The HCF of 840,906 is 6

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 840/827, 906/778?

Answer: GCF of Numerators as per given numbers 840/827, 906/778 is

GCF of Numerators i.e. for 840,906 is 6

LCM of denominators i.e. for 827,778 is 643406.

Thus, GCF of Fractions is 6/643406.Finally, GCF of Fractions for 840/827, 906/778 is 6/643406.