How to Find GCF of 822/260, 120/412?

GCF of 822/260, 120/412

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 822/260, 120/412 i.e 6/26780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 822/260, 120/412.

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 822/260,120/412?

Given fractions are 822/260,120/412

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 822/260,120/412, numerators are 822,120

Denominators are 260,412

The GCF of 822,120 is 6 .

LCM of 260,412 is 26780.

The greatest common factor of 822/260,120/412 = [GCF of 822,120]/[LCM of 260,412]= 6/26780

Therefore, the GCF of 822/260,120/412 is 6/26780.

Greatest Common Factor of 822,120

To find the highest common factor of 822,120, we have to find the factors of both numbers and list the highest common factor.

The factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The HCF of 822,120 is 6.

Lets's calculate GCF of 822,120

Greatest Common Factor (GCF) of 822,120 By Common Division

2	822, 120
3	411, 60
	137, 20

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

Greatest Common Factor of 822,120 By Matching Biggest Common Factor Method

Now, list down the factors of 822

1,2,3,6,137,274,411,822

Now, list down the factors of 120

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Greatest Common Factor

We found the factors 822,120 . The biggest common factor number is the GCF number.
So the greatest common factor 822,120 is 6.

Lets's calculate LCM of 260,412

Lowest Common Multiple of 260,412 using Common Division

2	260, 412
2	130, 206
	65, 103

∴ So the LCM of the given numbers is 2 x 2 x 65 x 103 = 26780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/26780

Therefore, the GCF of Fractions 822/260,120/412 is 6/26780

Least Common Multiple of 260,412 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 260,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(260,412) = 4

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

GCF(260,412) x common factors =4 x 1 = 4

LCM(260,412) = ( 260 × 412 ) / 4

LCM(260,412) = 107120 / 4

LCM(260,412) = 26780

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FAQs on GCF of Fractions of 822/260, 120/412

1. What is the HCF of 822,120?

The HCF of 822,120 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 822/260, 120/412?

Answer: GCF of Numerators as per given numbers 822/260, 120/412 is

GCF of Numerators i.e. for 822,120 is 6

LCM of denominators i.e. for 260,412 is 26780.

Thus, GCF of Fractions is 6/26780.Finally, GCF of Fractions for 822/260, 120/412 is 6/26780.