How to Find GCF of 222/164, 280/756?

GCF of 222/164, 280/756

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 222/164, 280/756 i.e 2/30996 easily. The following is the detailed procedure to determine the greatest common factor of fractions 222/164, 280/756.

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 222/164,280/756?

Given fractions are 222/164,280/756

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 222/164,280/756, numerators are 222,280

Denominators are 164,756

The GCF of 222,280 is 2 .

LCM of 164,756 is 30996.

The greatest common factor of 222/164,280/756 = [GCF of 222,280]/[LCM of 164,756]= 2/30996

Therefore, the GCF of 222/164,280/756 is 2/30996.

Greatest Common Factor of 222,280

To find the highest common factor of 222,280, we have to find the factors of both numbers and list the highest common factor.

The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222

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

The HCF of 222,280 is 2.

Lets's calculate GCF of 222,280

Greatest Common Factor (GCF) of 222,280 By Common Division

2	222, 280
	111, 140

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 222,280 By Matching Biggest Common Factor Method

Now, list down the factors of 222

1,2,3,6,37,74,111,222

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 222,280 . The biggest common factor number is the GCF number.
So the greatest common factor 222,280 is 2.

Lets's calculate LCM of 164,756

Lowest Common Multiple of 164,756 using Common Division

2	164, 756
2	82, 378
	41, 189

∴ So the LCM of the given numbers is 2 x 2 x 41 x 189 = 30996

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/30996

Therefore, the GCF of Fractions 222/164,280/756 is 2/30996

Least Common Multiple of 164,756 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 164,756 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(164,756) = 4

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

GCF(164,756) x common factors =4 x 1 = 4

LCM(164,756) = ( 164 × 756 ) / 4

LCM(164,756) = 123984 / 4

LCM(164,756) = 30996

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FAQs on GCF of Fractions of 222/164, 280/756

1. What is the HCF of 222,280?

The HCF of 222,280 is 2

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 222/164, 280/756?

Answer: GCF of Numerators as per given numbers 222/164, 280/756 is

GCF of Numerators i.e. for 222,280 is 2

LCM of denominators i.e. for 164,756 is 30996.

Thus, GCF of Fractions is 2/30996.Finally, GCF of Fractions for 222/164, 280/756 is 2/30996.