How to Find GCF of 972/191, 360/253?

GCF of 972/191, 360/253

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 972/191, 360/253 i.e 36/48323 easily. The following is the detailed procedure to determine the greatest common factor of fractions 972/191, 360/253.

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 972/191,360/253?

Given fractions are 972/191,360/253

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 972/191,360/253, numerators are 972,360

Denominators are 191,253

The GCF of 972,360 is 36 .

LCM of 191,253 is 48323.

The greatest common factor of 972/191,360/253 = [GCF of 972,360]/[LCM of 191,253]= 36/48323

Therefore, the GCF of 972/191,360/253 is 36/48323.

Greatest Common Factor of 972,360

To find the highest common factor of 972,360, 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 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

The HCF of 972,360 is 36.

Lets's calculate GCF of 972,360

Greatest Common Factor (GCF) of 972,360 By Common Division

2	972, 360
2	486, 180
3	243, 90
3	81, 30
	27, 10

∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36

Greatest Common Factor of 972,360 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 360

1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360

Greatest Common Factor

We found the factors 972,360 . The biggest common factor number is the GCF number.
So the greatest common factor 972,360 is 36.

Lets's calculate LCM of 191,253

Lowest Common Multiple of 191,253 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 48323

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/48323

Therefore, the GCF of Fractions 972/191,360/253 is 36/48323

Least Common Multiple of 191,253 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 191,253 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(191,253) = 1

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

GCF(191,253) x common factors =1 x 1 = 1

LCM(191,253) = ( 191 × 253 ) / 1

LCM(191,253) = 48323 / 1

LCM(191,253) = 48323

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FAQs on GCF of Fractions of 972/191, 360/253

1. What is the HCF of 972,360?

The HCF of 972,360 is 36

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 972/191, 360/253?

Answer: GCF of Numerators as per given numbers 972/191, 360/253 is

GCF of Numerators i.e. for 972,360 is 36

LCM of denominators i.e. for 191,253 is 48323.

Thus, GCF of Fractions is 36/48323.Finally, GCF of Fractions for 972/191, 360/253 is 36/48323.