How to Find GCF of 216/527, 900/264?

GCF of 216/527, 900/264

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 216/527, 900/264 i.e 36/139128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/527, 900/264.

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 216/527,900/264?

Given fractions are 216/527,900/264

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 216/527,900/264, numerators are 216,900

Denominators are 527,264

The GCF of 216,900 is 36 .

LCM of 527,264 is 139128.

The greatest common factor of 216/527,900/264 = [GCF of 216,900]/[LCM of 527,264]= 36/139128

Therefore, the GCF of 216/527,900/264 is 36/139128.

Greatest Common Factor of 216,900

To find the highest common factor of 216,900, we have to find the factors of both numbers and list the highest common factor.

The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900

The HCF of 216,900 is 36.

Lets's calculate GCF of 216,900

Greatest Common Factor (GCF) of 216,900 By Common Division

2	216, 900
2	108, 450
3	54, 225
3	18, 75
	6, 25

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

Greatest Common Factor of 216,900 By Matching Biggest Common Factor Method

Now, list down the factors of 216

1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216

Now, list down the factors of 900

1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900

Greatest Common Factor

We found the factors 216,900 . The biggest common factor number is the GCF number.
So the greatest common factor 216,900 is 36.

Lets's calculate LCM of 527,264

Lowest Common Multiple of 527,264 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 139128

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/139128

Therefore, the GCF of Fractions 216/527,900/264 is 36/139128

Least Common Multiple of 527,264 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 527,264 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(527,264) = 1

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

GCF(527,264) x common factors =1 x 1 = 1

LCM(527,264) = ( 527 × 264 ) / 1

LCM(527,264) = 139128 / 1

LCM(527,264) = 139128

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FAQs on GCF of Fractions of 216/527, 900/264

1. What is the HCF of 216,900?

The HCF of 216,900 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 216/527, 900/264?

Answer: GCF of Numerators as per given numbers 216/527, 900/264 is

GCF of Numerators i.e. for 216,900 is 36

LCM of denominators i.e. for 527,264 is 139128.

Thus, GCF of Fractions is 36/139128.Finally, GCF of Fractions for 216/527, 900/264 is 36/139128.