How to Find GCF of 90/888, 77/200, 120/214?

GCF of 90/888, 77/200, 120/214

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 90/888, 77/200, 120/214 i.e 1/2375400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 90/888, 77/200, 120/214.

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 90/888,77/200,120/214?

Given fractions are 90/888,77/200,120/214

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 90/888,77/200,120/214, numerators are 90,77,120

Denominators are 888,200,214

The GCF of 90,77,120 is 1 .

LCM of 888,200,214 is 2375400.

The greatest common factor of 90/888,77/200,120/214 = [GCF of 90,77,120]/[LCM of 888,200,214]= 1/2375400

Therefore, the GCF of 90/888,77/200,120/214 is 1/2375400.

Greatest Common Factor of 90,77,120

To find the highest common factor of 90,77,120, we have to find the factors of both numbers and list the highest common factor.

The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

The factors of 77 are 1, 7, 11, 77

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

The HCF of 90,77,120 is 1.

Lets's calculate GCF of 90,77,120

Greatest Common Factor (GCF) of 90,77,120 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 90,77,120 By Matching Biggest Common Factor Method

Now, list down the factors of 90

1,2,3,5,6,9,10,15,18,30,45,90

Now, list down the factors of 77

1,7,11,77

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 90,77,120 . The biggest common factor number is the GCF number.
So the greatest common factor 90,77,120 is 1.

Lets's calculate LCM of 888,200,214

Lowest Common Multiple of 888,200,214 using Common Division

2	888, 200, 214
2	444, 100, 107
2	222, 50, 107
	111, 25, 107

∴ So the LCM of the given numbers is 2 x 2 x 2 x 111 x 25 x 107 = 2375400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2375400

Therefore, the GCF of Fractions 90/888,77/200,120/214 is 1/2375400

Least Common Multiple of 888,200,214 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 888,200,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(888,200,214) = 2

common factors(in case of two or more numbers have common factors) = 8

GCF(888,200,214) x common factors =2 x 8 = 16

LCM(888,200,214) = ( 888 × 200 × 214 ) / 16

LCM(888,200,214) = 38006400 / 16

LCM(888,200,214) = 2375400

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 90/888, 77/200, 120/214

1. What is the HCF of 90,77,120?

The HCF of 90,77,120 is 1

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 90/888, 77/200, 120/214?

Answer: GCF of Numerators as per given numbers 90/888, 77/200, 120/214 is

GCF of Numerators i.e. for 90,77,120 is 1

LCM of denominators i.e. for 888,200,214 is 2375400.

Thus, GCF of Fractions is 1/2375400.Finally, GCF of Fractions for 90/888, 77/200, 120/214 is 1/2375400.