How to Find GCF of 212/425, 960/756?

GCF of 212/425, 960/756

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 212/425, 960/756 i.e 4/321300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 212/425, 960/756.

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 212/425,960/756?

Given fractions are 212/425,960/756

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 212/425,960/756, numerators are 212,960

Denominators are 425,756

The GCF of 212,960 is 4 .

LCM of 425,756 is 321300.

The greatest common factor of 212/425,960/756 = [GCF of 212,960]/[LCM of 425,756]= 4/321300

Therefore, the GCF of 212/425,960/756 is 4/321300.

Greatest Common Factor of 212,960

To find the highest common factor of 212,960, we have to find the factors of both numbers and list the highest common factor.

The factors of 212 are 1, 2, 4, 53, 106, 212

The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960

The HCF of 212,960 is 4.

Lets's calculate GCF of 212,960

Greatest Common Factor (GCF) of 212,960 By Common Division

2	212, 960
2	106, 480
	53, 240

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 212,960 By Matching Biggest Common Factor Method

Now, list down the factors of 212

1,2,4,53,106,212

Now, list down the factors of 960

1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960

Greatest Common Factor

We found the factors 212,960 . The biggest common factor number is the GCF number.
So the greatest common factor 212,960 is 4.

Lets's calculate LCM of 425,756

Lowest Common Multiple of 425,756 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 321300

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/321300

Therefore, the GCF of Fractions 212/425,960/756 is 4/321300

Least Common Multiple of 425,756 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 425,756 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(425,756) = 1

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

GCF(425,756) x common factors =1 x 1 = 1

LCM(425,756) = ( 425 × 756 ) / 1

LCM(425,756) = 321300 / 1

LCM(425,756) = 321300

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FAQs on GCF of Fractions of 212/425, 960/756

1. What is the HCF of 212,960?

The HCF of 212,960 is 4

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 212/425, 960/756?

Answer: GCF of Numerators as per given numbers 212/425, 960/756 is

GCF of Numerators i.e. for 212,960 is 4

LCM of denominators i.e. for 425,756 is 321300.

Thus, GCF of Fractions is 4/321300.Finally, GCF of Fractions for 212/425, 960/756 is 4/321300.