How to Find GCF of 154/589, 280/863?

GCF of 154/589, 280/863

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 154/589, 280/863 i.e 14/508307 easily. The following is the detailed procedure to determine the greatest common factor of fractions 154/589, 280/863.

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 154/589,280/863?

Given fractions are 154/589,280/863

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 154/589,280/863, numerators are 154,280

Denominators are 589,863

The GCF of 154,280 is 14 .

LCM of 589,863 is 508307.

The greatest common factor of 154/589,280/863 = [GCF of 154,280]/[LCM of 589,863]= 14/508307

Therefore, the GCF of 154/589,280/863 is 14/508307.

Greatest Common Factor of 154,280

To find the highest common factor of 154,280, we have to find the factors of both numbers and list the highest common factor.

The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154

The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280

The HCF of 154,280 is 14.

Lets's calculate GCF of 154,280

Greatest Common Factor (GCF) of 154,280 By Common Division

2	154, 280
7	77, 140
	11, 20

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 154,280 By Matching Biggest Common Factor Method

Now, list down the factors of 154

1,2,7,11,14,22,77,154

Now, list down the factors of 280

1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280

Greatest Common Factor

We found the factors 154,280 . The biggest common factor number is the GCF number.
So the greatest common factor 154,280 is 14.

Lets's calculate LCM of 589,863

Lowest Common Multiple of 589,863 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 508307

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/508307

Therefore, the GCF of Fractions 154/589,280/863 is 14/508307

Least Common Multiple of 589,863 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 589,863 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(589,863) = 1

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

GCF(589,863) x common factors =1 x 1 = 1

LCM(589,863) = ( 589 × 863 ) / 1

LCM(589,863) = 508307 / 1

LCM(589,863) = 508307

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FAQs on GCF of Fractions of 154/589, 280/863

1. What is the HCF of 154,280?

The HCF of 154,280 is 14

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 154/589, 280/863?

Answer: GCF of Numerators as per given numbers 154/589, 280/863 is

GCF of Numerators i.e. for 154,280 is 14

LCM of denominators i.e. for 589,863 is 508307.

Thus, GCF of Fractions is 14/508307.Finally, GCF of Fractions for 154/589, 280/863 is 14/508307.