How to Find GCF of 972/237, 812/353?

GCF of 972/237, 812/353

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 972/237, 812/353 i.e 4/83661 easily. The following is the detailed procedure to determine the greatest common factor of fractions 972/237, 812/353.

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 972/237,812/353?

Given fractions are 972/237,812/353

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 972/237,812/353, numerators are 972,812

Denominators are 237,353

The GCF of 972,812 is 4 .

LCM of 237,353 is 83661.

The greatest common factor of 972/237,812/353 = [GCF of 972,812]/[LCM of 237,353]= 4/83661

Therefore, the GCF of 972/237,812/353 is 4/83661.

Greatest Common Factor of 972,812

To find the highest common factor of 972,812, we have to find the factors of both numbers and list the highest common factor.

The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972

The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812

The HCF of 972,812 is 4.

Lets's calculate GCF of 972,812

Greatest Common Factor (GCF) of 972,812 By Common Division

2	972, 812
2	486, 406
	243, 203

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

Greatest Common Factor of 972,812 By Matching Biggest Common Factor Method

Now, list down the factors of 972

1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972

Now, list down the factors of 812

1,2,4,7,14,28,29,58,116,203,406,812

Greatest Common Factor

We found the factors 972,812 . The biggest common factor number is the GCF number.
So the greatest common factor 972,812 is 4.

Lets's calculate LCM of 237,353

Lowest Common Multiple of 237,353 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 83661

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/83661

Therefore, the GCF of Fractions 972/237,812/353 is 4/83661

Least Common Multiple of 237,353 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 237,353 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(237,353) = 1

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

GCF(237,353) x common factors =1 x 1 = 1

LCM(237,353) = ( 237 × 353 ) / 1

LCM(237,353) = 83661 / 1

LCM(237,353) = 83661

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FAQs on GCF of Fractions of 972/237, 812/353

1. What is the HCF of 972,812?

The HCF of 972,812 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 972/237, 812/353?

Answer: GCF of Numerators as per given numbers 972/237, 812/353 is

GCF of Numerators i.e. for 972,812 is 4

LCM of denominators i.e. for 237,353 is 83661.

Thus, GCF of Fractions is 4/83661.Finally, GCF of Fractions for 972/237, 812/353 is 4/83661.